Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
314 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 314 conjugacy classes of subgroups — too many to draw. Only its 71 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. #11736860 | C2 | semidirect |
| 3. #11727046 | C2 | semidirect |
| 4. #11726812 | C2 | semidirect |
| 5. C7×D4⋊C16 | C2 | semidirect |
| 6. #11725371 | C2 | semidirect |
| 7. #11725311 | C2 | semidirect |
| 60. D4⋊C16 | D7 | semidirect |
| 114. C7×D4 | SD32 | semidirect |
| 231. D4 | #6374 | semidirect |
| 247. C7 | #12342 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11736860 | 2 |
| #11728601 | 2 |
| #11727046 | 2 |
| #11726812 | 2 |
| C7×D4⋊C16 | 2 |
| #11725371 | 2 |
| #11725311 | 2 |
| #12342 | 7 |