Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
568 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 568 conjugacy classes of subgroups — too many to draw. Only its 93 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. #11741359 | C2 | semidirect |
| 2. #11741339 | C2 | semidirect |
| 3. #11736625 | C2 | semidirect |
| 4. C7×#2145 | C2 | semidirect |
| 5. #11729204 | C2 | semidirect |
| 6. #11729185 | C2 | semidirect |
| 7. #11725531 | C2 | semidirect |
| 41. C2×C7×Q16 | D4 | semidirect |
| 43. C2×C7×D8 | D4 | semidirect |
| 53. C2×Dic28 | D4 | semidirect |
| 58. C2×D56 | D4 | semidirect |
| 75. C7×#106 | D4 | semidirect |
| 83. #6391 | D4 | semidirect |
| 86. C2×C7⋊C16 | D4 | semidirect |
| 93. #2145 | D7 | semidirect |
| 246. C2×Q16 | D28 | semidirect |
| 250. C2×D8 | D28 | semidirect |
| 284. #106 | C22⋊D7 | semidirect |
| 433. C7 | #13309 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11741359 | 2 |
| #11741339 | 2 |
| #11736625 | 2 |
| C7×#2145 | 2 |
| #11729204 | 2 |
| #11729185 | 2 |
| #11725531 | 2 |
| #13309 | 7 |