Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
480 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 480 conjugacy classes of subgroups — too many to draw. Only its 99 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×#2995 | C2 | semidirect |
| 3. #11729501 | C2 | semidirect |
| 4. #11728572 | C2 | semidirect |
| 5. #11728275 | C2 | semidirect |
| 6. #11725559 | C2 | semidirect |
| 7. #11725522 | C2 | semidirect |
| 84. #2995 | D7 | semidirect |
| 376. C7 | #9340 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×#2995 | 2 |
| #11740591 | 2 |
| #11729501 | 2 |
| #11728572 | 2 |
| #11728275 | 2 |
| #11725559 | 2 |
| #11725522 | 2 |
| #9340 | 7 |