Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
354 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 354 conjugacy classes of subgroups — too many to draw. Only its 95 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. C7×#2248 | C2 | semidirect |
| 2. #11729067 | C2 | semidirect |
| 3. #11729052 | C2 | semidirect |
| 4. #11729045 | C2 | semidirect |
| 6. #11726815 | C2 | semidirect |
| 7. C16×C7⋊C8 | C2 | semidirect |
| 47. #2248 | D7 | semidirect |
| 72. C7×C16 | D8 | semidirect |
| 73. C7⋊C16 | D8 | semidirect |
| 105. C7⋊C8 | SD32 | semidirect |
| 160. C16 | #1141 | semidirect |
| 184. C7 | #12517 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×#2248 | 2 |
| #11729067 | 2 |
| #11729052 | 2 |
| #11729045 | 2 |
| #11729030 | 2 |
| #11726815 | 2 |
| C16×C7⋊C8 | 2 |
| #12517 | 7 |