Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
398 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 398 conjugacy classes of subgroups — too many to draw. Only its 93 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. C7×#1518 | C2 | semidirect |
| 3. #11729582 | C2 | semidirect |
| 5. #11728503 | C2 | semidirect |
| 7. #11725437 | C2 | semidirect |
| 69. #1518 | D7 | semidirect |
| 316. C7 | #10468 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11740795 | 2 |
| C7×#1518 | 2 |
| #11729582 | 2 |
| #11728537 | 2 |
| #11728503 | 2 |
| #11727310 | 2 |
| #11725437 | 2 |
| #10468 | 7 |