Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
574 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 574 conjugacy classes of subgroups — too many to draw. Only its 85 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. #26021586 | C2 | semidirect |
| 3. #26021388 | C2 | semidirect |
| 4. #26021337 | C2 | semidirect |
| 5. #26018074 | C2 | semidirect |
| 6. #26018072 | C2 | semidirect |
| 7. C89×#1270 | C2 | semidirect |
| 101. C4⋊Dic89 | SD16 | semidirect |
| 115. C2×D4×C89 | SD16 | semidirect |
| 236. #1270 | D89 | semidirect |
| 237. C89 | #7778 | semidirect |
| 316. C2×D4 | #13083563 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26026616 | 2 |
| #26021586 | 2 |
| #26021388 | 2 |
| #26021337 | 2 |
| #26018074 | 2 |
| #26018072 | 2 |
| C89×#1270 | 2 |
| #7778 | 89 |