Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
402 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 402 conjugacy classes of subgroups — too many to draw. Only its 107 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 |
|---|---|---|
| 2. C4×#15667951 | C2 | semidirect |
| 3. #335×D89 | C2 | semidirect |
| 4. #26018217 | C2 | semidirect |
| 5. #26018215 | C2 | semidirect |
| 6. #26018213 | C2 | semidirect |
| 7. C89×#1331 | C2 | semidirect |
| 29. #15668031 | C8 | semidirect |
| 73. Dic356 | C2×C8 | semidirect |
| 97. D8×C89 | C2×C8 | semidirect |
| 167. #1331 | D89 | semidirect |
| 168. C89 | #11592 | semidirect |
| 239. D8 | C8×D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#15668031 | 2 |
| C4×#15667951 | 2 |
| #335×D89 | 2 |
| #26018217 | 2 |
| #26018215 | 2 |
| #26018213 | 2 |
| C89×#1331 | 2 |
| #11592 | 89 |