Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
402 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 402 conjugacy classes of subgroups — too many to draw. Only its 105 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 |
|---|---|---|
| 2. #11726825 | C2 | semidirect |
| 3. D7×#334 | C2 | semidirect |
| 4. C7×#1334 | C2 | semidirect |
| 5. #11725570 | C2 | semidirect |
| 6. #11725322 | C2 | semidirect |
| 7. #11725271 | C2 | semidirect |
| 34. #6482 | C8 | semidirect |
| 68. #1334 | D7 | semidirect |
| 83. C7×Q16 | C2×C8 | semidirect |
| 106. D56 | C2×C8 | semidirect |
| 227. Q16 | C8×D7 | semidirect |
| 292. C7 | #11598 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#6482 | 2 |
| #11726825 | 2 |
| D7×#334 | 2 |
| C7×#1334 | 2 |
| #11725570 | 2 |
| #11725322 | 2 |
| #11725271 | 2 |
| #11598 | 7 |