Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
492 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 109 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. #26028844 | C2 | semidirect |
| 3. C2×#19151408 | C2 | semidirect |
| 4. #26021881 | C2 | semidirect |
| 5. #26018368 | C2 | semidirect |
| 6. #26018351 | C2 | semidirect |
| 7. C89×#2145 | C2 | semidirect |
| 12. #19151870 | C4 | semidirect |
| 13. #19151865 | C4 | semidirect |
| 53. #15667948 | C2×C4 | semidirect |
| 65. C2×Q16×C89 | C2×C4 | semidirect |
| 67. C2×D8×C89 | C2×C4 | semidirect |
| 196. #2145 | D89 | semidirect |
| 201. C89 | #13005 | semidirect |
| 234. C2×Q16 | C4×D89 | semidirect |
| 236. C2×D8 | C4×D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26029968 | 2 |
| #26028844 | 2 |
| C2×#19151408 | 2 |
| #26021881 | 2 |
| #26018368 | 2 |
| #26018351 | 2 |
| C89×#2145 | 2 |
| #13005 | 89 |