Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
232 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 232 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 |
|---|---|---|
| 4. C7×#1367 | C2 | semidirect |
| 5. #11725361 | C2 | semidirect |
| 6. #11725360 | C2 | semidirect |
| 7. #11725246 | C2 | semidirect |
| 52. #1367 | D7 | semidirect |
| 109. C7×C8 | M32 | semidirect |
| 116. C7⋊C8 | M32 | semidirect |
| 201. C8 | #6372 | semidirect |
| 204. C7 | #12017 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11727038 | 2 |
| #11727029 | 2 |
| C8×#1131 | 2 |
| C7×#1367 | 2 |
| #11725361 | 2 |
| #11725360 | 2 |
| #11725246 | 2 |
| #12017 | 7 |