Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
568 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 568 conjugacy classes of subgroups — too many to draw. Only its 91 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. #11736780 | C2 | semidirect |
| 3. #11728581 | C2 | semidirect |
| 4. #11728562 | C2 | semidirect |
| 5. #11728562 | C2 | semidirect |
| 6. C7×#1285 | C2 | semidirect |
| 7. #11725427 | C2 | semidirect |
| 69. C7×#97 | D4 | semidirect |
| 80. #6377 | D4 | semidirect |
| 87. #1285 | D7 | semidirect |
| 275. #97 | D28 | semidirect |
| 439. C7 | #9447 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11736780 | 2 |
| #11731246 | 2 |
| #11728581 | 2 |
| #11728562 | 2 |
| C7×#1285 | 2 |
| #11725427 | 2 |
| #9447 | 7 |