Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
552 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 552 conjugacy classes of subgroups — too many to draw. Only its 95 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×C7×#509 | C2 | semidirect |
| 2. #11741373 | C2 | semidirect |
| 3. #11741281 | C2 | semidirect |
| 4. #11729830 | C2 | semidirect |
| 5. C2×#89358 | C2 | semidirect |
| 6. #11729192 | C2 | semidirect |
| 7. #11725628 | C2 | semidirect |
| 39. C2×C7×Q16 | D4 | semidirect |
| 47. C2×C7×D8 | D4 | semidirect |
| 70. C7×M32 | D4 | semidirect |
| 76. #6393 | D4 | semidirect |
| 82. C2×#509 | D7 | semidirect |
| 228. C2×Q16 | C22⋊D7 | semidirect |
| 236. C2×D8 | C22⋊D7 | semidirect |
| 256. M32 | C22⋊D7 | semidirect |
| 396. C7 | #13310 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C7×#509 | 2 |
| #11741373 | 2 |
| #11741281 | 2 |
| #11729830 | 2 |
| C2×#89358 | 2 |
| #11729192 | 2 |
| #11725628 | 2 |
| #13310 | 7 |