Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
4382 conjugacy classes of subgroups; only the 590 normal subgroups are shown.
This group has 4382 conjugacy classes of subgroups — too many to draw. Only its 590 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C24×C7 | C24 |
| commutator, Frattini, cosocle | C24 | C24×C7 |
| LCS | G ▷ C24 ▷ C1 | |
| UCS | C1 ◁ C24×C7 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C22×C7×#127 | C2 | semidirect |
| 2. C2×C7×#392 | C2 | semidirect |
| 3. C2×C7×#390 | C2 | semidirect |
| 4. C4×C7×#95 | C2 | semidirect |
| 15. #15142 | C7 | direct (N × H) |
| 25. C22×C7×D4 | D4 | semidirect |
| 34. C2×C42×C7 | D4 | semidirect |
| 35. C7×#95 | D4 | semidirect |
| 36. C22×#127 | C2×C7 | semidirect |
| 37. C2×#392 | C2×C7 | semidirect |
| 38. C2×#390 | C2×C7 | semidirect |
| 39. C4×#95 | C2×C7 | semidirect |
| 106. C2×C4×C7 | #127 | semidirect |
| 116. C22×D4 | C7×D4 | semidirect |
| 125. C2×C42 | C7×D4 | semidirect |
| 126. #95 | C7×D4 | semidirect |
| 143. C4×C7 | #392 | semidirect |
| 206. C2×C4 | C7×#127 | semidirect |
| 207. C7 | #15142 | direct (N × H) |
| 224. C4 | C7×#392 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C7×#127 | 2 |
| C2×C7×#392 | 2 |
| C2×C7×#390 | 2 |
| C4×C7×#95 | 2 |
| #15142 | 7 |