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. #26018216 | C2 | semidirect |
| 5. #26018214 | C2 | semidirect |
| 6. #26018212 | C2 | semidirect |
| 7. C89×#1332 | C2 | semidirect |
| 29. #15668035 | C8 | semidirect |
| 75. D712 | C2×C8 | semidirect |
| 96. Q16×C89 | C2×C8 | semidirect |
| 165. #1332 | D89 | semidirect |
| 168. C89 | #11592 | semidirect |
| 236. Q16 | C8×D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#15668035 | 2 |
| C4×#15667951 | 2 |
| #335×D89 | 2 |
| #26018216 | 2 |
| #26018214 | 2 |
| #26018212 | 2 |
| C89×#1332 | 2 |
| #11592 | 89 |