Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
678 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 678 conjugacy classes of subgroups — too many to draw. Only its 109 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. C7×#3226 | C2 | semidirect |
| 3. #11740696 | C2 | semidirect |
| 4. #11729569 | C2 | semidirect |
| 5. #11729527 | C2 | semidirect |
| 6. #11728528 | C2 | semidirect |
| 7. #11725542 | C2 | semidirect |
| 73. #3226 | D7 | semidirect |
| 126. C4×Dic7 | D8 | semidirect |
| 355. C7 | #10284 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×#3226 | 2 |
| #11740747 | 2 |
| #11740696 | 2 |
| #11729569 | 2 |
| #11729527 | 2 |
| #11728528 | 2 |
| #11725542 | 2 |
| #10284 | 7 |