Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
6020 conjugacy classes of subgroups; only the 438 normal subgroups are shown.
This group has 6020 conjugacy classes of subgroups — too many to draw. Only its 438 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C7 | C22×D4 |
| commutator, Frattini, cosocle | C22×C4 | C24×C7 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C7 ◁ C24×C4×C7 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C24×C7×D4 | C2 | semidirect |
| 2. C2×C7×#447 | C2 | semidirect |
| 3. C7×#2847 | C2 | semidirect |
| 4. C7×#1786 | C2 | semidirect |
| 5. C7×#1779 | C2 | semidirect |
| 11. C22×C7×D8 | C22 | semidirect |
| 12. C2×C7×#121 | C22 | semidirect |
| 15. C2×C7×#102 | C22 | semidirect |
| 16. C2×C7×C22⋊C8 | C22 | semidirect |
| 18. C7×#380 | C22 | semidirect |
| 19. #32878 | C7 | direct (N × H) |
| 32. C22×C7×D4 | D4 | semidirect |
| 34. C22×C7×D4 | C23 | semidirect |
| 39. C22×C7×C8 | C23 | semidirect |
| 42. C2×C7×C4⋊C4 | C23 | semidirect |
| 48. C24×D4 | C2×C7 | semidirect |
| 49. C2×#447 | C2×C7 | semidirect |
| 50. #2847 | C2×C7 | semidirect |
| 51. #1786 | C2×C7 | semidirect |
| 52. #1779 | C2×C7 | semidirect |
| 65. C24×C7 | D8 | semidirect |
| 96. C22×D8 | C22×C7 | semidirect |
| 97. C2×#121 | C22×C7 | semidirect |
| 100. C2×#102 | C22×C7 | semidirect |
| 101. C2×C22⋊C8 | C22×C7 | semidirect |
| 103. #380 | C22×C7 | semidirect |
| 129. C7×D4 | #120 | semidirect |
| 151. C22×D4 | C7×D4 | semidirect |
| 153. C22×D4 | C23×C7 | semidirect |
| 158. C22×C8 | C23×C7 | semidirect |
| 161. C2×C4⋊C4 | C23×C7 | semidirect |
| 179. C22×C7 | #447 | semidirect |
| 198. C24 | C7×D8 | semidirect |
| 255. D4 | C7×#120 | semidirect |
| 265. C7 | #32878 | direct (N × H) |
| 278. C22 | C7×#447 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C24×C7×D4 | 2 |
| C2×C7×#447 | 2 |
| C7×#2847 | 2 |
| C7×#1786 | 2 |
| C7×#1779 | 2 |
| #32878 | 7 |