Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
602 conjugacy classes of subgroups; only the 155 normal subgroups are shown.
This group has 602 conjugacy classes of subgroups — too many to draw. Only its 155 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. #11739378 | C2 | semidirect |
| 2. C7×#2252 | C2 | semidirect |
| 3. #11729135 | C2 | semidirect |
| 4. #11727081 | C2 | semidirect |
| 5. #11727071 | C2 | semidirect |
| 6. #11726814 | C2 | semidirect |
| 7. C4×D7×C16 | C2 | semidirect |
| 51. #2252 | D7 | semidirect |
| 83. C7×C16 | #41 | semidirect |
| 120. C4×D7 | D16 | semidirect |
| 192. C16 | #1161 | semidirect |
| 222. C7 | #33733 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11739378 | 2 |
| C7×#2252 | 2 |
| #11729135 | 2 |
| #11727081 | 2 |
| #11727071 | 2 |
| #11726814 | 2 |
| C4×D7×C16 | 2 |
| #33733 | 7 |