Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
632 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 632 conjugacy classes of subgroups — too many to draw. Only its 107 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. #11731598 | C2 | semidirect |
| 3. C7×#1517 | C2 | semidirect |
| 4. #11729570 | C2 | semidirect |
| 5. #11728528 | C2 | semidirect |
| 6. #11725543 | C2 | semidirect |
| 7. #11725437 | C2 | semidirect |
| 15. #89860 | C4 | semidirect |
| 16. #89845 | C4 | semidirect |
| 33. C7×C4⋊Q8 | C2×C4 | semidirect |
| 34. C7×#127 | C2×C4 | semidirect |
| 69. C4×C7⋊C8 | C2×C4 | semidirect |
| 74. #1517 | D7 | semidirect |
| 127. C4×Dic7 | D8 | semidirect |
| 211. C4⋊Q8 | C4×D7 | semidirect |
| 216. #127 | C4×D7 | semidirect |
| 388. C7 | #9299 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11740747 | 2 |
| #11731598 | 2 |
| C7×#1517 | 2 |
| #11729570 | 2 |
| #11728528 | 2 |
| #11725543 | 2 |
| #11725437 | 2 |
| #9299 | 7 |