Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
530 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 530 conjugacy classes of subgroups — too many to draw. Only its 105 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 |
|---|---|---|
| 3. C7×#1960 | C2 | semidirect |
| 4. #11729542 | C2 | semidirect |
| 6. #11725465 | C2 | semidirect |
| 7. #11725436 | C2 | semidirect |
| 15. #89861 | C4 | semidirect |
| 39. C7×C4⋊Q8 | C2×C4 | semidirect |
| 75. #6377 | C2×C4 | semidirect |
| 79. #1960 | D7 | semidirect |
| 222. C4⋊Q8 | C4×D7 | semidirect |
| 398. C7 | #8999 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#89861 | 2 |
| #11731675 | 2 |
| C7×#1960 | 2 |
| #11729542 | 2 |
| C2×#89259 | 2 |
| #11725465 | 2 |
| #11725436 | 2 |
| #8999 | 7 |