Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
552 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 552 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. #11741281 | C2 | semidirect |
| 2. C2×#89919 | C2 | semidirect |
| 3. #11736701 | C2 | semidirect |
| 4. C2×C7×#361 | C2 | semidirect |
| 5. #11729204 | C2 | semidirect |
| 6. #11729191 | C2 | semidirect |
| 7. #11725541 | C2 | semidirect |
| 53. C2×Dic28 | D4 | semidirect |
| 59. C2×D56 | D4 | semidirect |
| 71. C7×#108 | D4 | semidirect |
| 80. #6386 | D4 | semidirect |
| 85. C2×#361 | D7 | semidirect |
| 260. #108 | C22⋊D7 | semidirect |
| 396. C7 | #13310 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11741281 | 2 |
| C2×#89919 | 2 |
| #11736701 | 2 |
| C2×C7×#361 | 2 |
| #11729204 | 2 |
| #11729191 | 2 |
| #11725541 | 2 |
| #13310 | 7 |