Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
8094 conjugacy classes of subgroups; only the 1243 normal subgroups are shown.
This group has 8094 conjugacy classes of subgroups — too many to draw. Only its 1243 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C24 | C23×D7 |
| commutator, cosocle | C23×C7 | C25 |
| Frattini | C23 | C24×D7 |
| Fitting | C22×C7×#127 | C2 |
| socle | C24×C7 | C24 |
| hypercenter | C22×#127 | D7 |
| hypocenter | C7 | C2×#2867 |
| LCS | G ▷ C23×C7 ▷ C7 | |
| UCS | C1 ◁ C24 ◁ C22×#127 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C22×C7×#127 | C2 | semidirect |
| 2. C22×#6503 | C2 | semidirect |
| 3. C22×#6437 | C2 | semidirect |
| 4. #11740630 | C2 | direct (N × H) |
| 5. C2×C42×Dic7 | C2 | semidirect |
| 10. C2×C7×#127 | C22 | semidirect |
| 13. C2×#6503 | C22 | semidirect |
| 16. C2×#6437 | C22 | semidirect |
| 17. C42×Dic7 | C22 | semidirect |
| 32. C2×C42×C7 | D4 | semidirect |
| 35. C2×C4×Dic7 | D4 | semidirect |
| 40. C22×#127 | D7 | semidirect |
| 63. C42×C7 | C2×D4 | semidirect |
| 64. C4×Dic7 | C2×D4 | semidirect |
| 73. C2×#127 | C2×D7 | semidirect |
| 89. C2×C4×C7 | #127 | semidirect |
| 93. C2×Dic7 | #127 | semidirect |
| 113. C2×C42 | C22⋊D7 | semidirect |
| 125. C4×C7 | C2×#127 | semidirect |
| 126. Dic7 | C2×#127 | semidirect |
| 148. C42 | C2×C22⋊D7 | semidirect |
| 150. C2×C7 | #2867 | semidirect |
| 170. C2×C4 | #6503 | semidirect |
| 173. C7 | C2×#2867 | semidirect |
| 185. C4 | C2×#6503 | semidirect |
| 188. C2 | #11740630 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C7×#127 | 2 |
| C22×#6503 | 2 |
| C22×#6437 | 2 |
| #11740630 | 2 |
| C2×C42×Dic7 | 2 |
| C2×#2867 | 7 |