Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
552 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 552 conjugacy classes of subgroups — too many to draw. Only its 97 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×#3058 | C2 | semidirect |
| 2. C2×#89919 | C2 | semidirect |
| 3. #11741250 | C2 | semidirect |
| 4. C2×#89358 | C2 | semidirect |
| 5. #11729760 | C2 | semidirect |
| 6. #11728410 | C2 | semidirect |
| 7. #11725533 | C2 | semidirect |
| 60. C2×Dic28 | D4 | semidirect |
| 65. C2×D56 | D4 | semidirect |
| 75. #6393 | D4 | semidirect |
| 79. #6386 | D4 | semidirect |
| 84. #3058 | D7 | semidirect |
| 396. C7 | #13310 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×#3058 | 2 |
| C2×#89919 | 2 |
| #11741250 | 2 |
| C2×#89358 | 2 |
| #11729760 | 2 |
| #11728410 | 2 |
| #11725533 | 2 |
| #13310 | 7 |