Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
602 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 602 conjugacy classes of subgroups — too many to draw. Only its 79 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. #26030193 | C2 | semidirect |
| 2. #26030188 | C2 | semidirect |
| 4. #26020327 | C2 | semidirect |
| 5. #26018780 | C2 | semidirect |
| 6. #26018161 | C2 | semidirect |
| 7. C89×#1510 | C2 | semidirect |
| 46. C2×C4⋊Dic89 | D4 | semidirect |
| 47. C2×C4⋊Dic89 | D4 | semidirect |
| 63. C22⋊#10623494 | D4 | semidirect |
| 79. C22⋊C8×C89 | D4 | semidirect |
| 233. #1510 | D89 | semidirect |
| 235. C89 | #9983 | semidirect |
| 304. C22⋊C8 | C22⋊D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26030193 | 2 |
| #26030188 | 2 |
| #26028274 | 2 |
| #26020327 | 2 |
| #26018780 | 2 |
| #26018161 | 2 |
| C89×#1510 | 2 |
| #9983 | 89 |