Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
4886 conjugacy classes of subgroups; only the 907 normal subgroups are shown.
This group has 4886 conjugacy classes of subgroups — too many to draw. Only its 907 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×#95 | C2 |
| socle | C24×C7 | C24 |
| hypercenter | C22×#95 | D7 |
| hypocenter | C7 | C2×#2656 |
| LCS | G ▷ C23×C7 ▷ C7 | |
| UCS | C1 ◁ C24 ◁ C22×#95 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C22×#6493 | C2 | semidirect |
| 2. C22×C7×#95 | C2 | semidirect |
| 3. #11730826 | C2 | direct (N × H) |
| 4. C2×#89449 | C2 | semidirect |
| 5. C2×#89443 | C2 | semidirect |
| 10. C2×#6493 | C22 | semidirect |
| 14. C2×C7×#95 | C22 | semidirect |
| 15. #89449 | C22 | semidirect |
| 16. #89443 | C22 | semidirect |
| 21. C23×C4×C7 | D4 | semidirect |
| 40. C22×#95 | D7 | semidirect |
| 54. C22×C4×C7 | C2×D4 | semidirect |
| 75. C2×#95 | C2×D7 | semidirect |
| 109. C23×C4 | D28 | semidirect |
| 154. C22×C4 | C2×D28 | semidirect |
| 159. C2×C7 | #2656 | semidirect |
| 188. C7 | C2×#2656 | semidirect |
| 207. C2 | #11730826 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#6493 | 2 |
| C22×C7×#95 | 2 |
| #11730826 | 2 |
| C2×#89449 | 2 |
| C2×#89443 | 2 |
| C2×#2656 | 7 |