Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
552 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 552 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 |
|---|---|---|
| 1. #11741339 | C2 | semidirect |
| 2. #11735944 | C2 | semidirect |
| 3. C7×#1975 | C2 | semidirect |
| 4. #11728444 | C2 | semidirect |
| 5. #11725469 | C2 | semidirect |
| 28. C2×C7×Q16 | D4 | semidirect |
| 30. C2×C7×D8 | D4 | semidirect |
| 62. C2×C7⋊C16 | D4 | semidirect |
| 66. #1975 | D7 | semidirect |
| 177. C2×Q16 | D28 | semidirect |
| 183. C2×D8 | D28 | semidirect |
| 305. C7 | #13340 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11741339 | 2 |
| #11735944 | 2 |
| C7×#1975 | 2 |
| #11728444 | 2 |
| #11725469 | 2 |
| #13340 | 7 |