Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
1230 conjugacy classes of subgroups; only the 355 normal subgroups are shown.
This group has 1230 conjugacy classes of subgroups — too many to draw. Only its 355 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. C2×#89460 | C2 | semidirect |
| 3. C42×C7×C8 | C2 | semidirect |
| 4. #11727541 | C2 | semidirect |
| 5. #11727148 | C2 | semidirect |
| 33. C4×C7×C8 | D4 | semidirect |
| 40. C42×C8 | D7 | semidirect |
| 55. C42×C7 | M16 | semidirect |
| 89. C7×C8 | #127 | semidirect |
| 108. C4×C8 | D28 | semidirect |
| 116. C4×C7 | #436 | semidirect |
| 138. C42 | #1131 | semidirect |
| 162. C8 | #6437 | semidirect |
| 163. C7 | #21681 | semidirect |
| 172. C4 | #89460 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#89460 | 2 |
| C4×#6437 | 2 |
| C42×C7×C8 | 2 |
| #11727541 | 2 |
| #11727148 | 2 |
| #21681 | 7 |