Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
602 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 602 conjugacy classes of subgroups — too many to draw. Only its 81 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. #26030192 | C2 | semidirect |
| 3. #26020329 | C2 | semidirect |
| 4. #26018782 | C2 | semidirect |
| 5. #26018781 | C2 | semidirect |
| 6. #26018161 | C2 | semidirect |
| 7. C89×#3094 | C2 | semidirect |
| 52. C22⋊#10623494 | D4 | semidirect |
| 71. C2×C4⋊C4×C89 | D4 | semidirect |
| 72. C2×C4⋊C4×C89 | D4 | semidirect |
| 81. C22⋊C8×C89 | D4 | semidirect |
| 229. #3094 | D89 | semidirect |
| 235. C89 | #9983 | semidirect |
| 283. C2×C4⋊C4 | C22⋊D89 | semidirect |
| 284. C2×C4⋊C4 | C22⋊D89 | 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 |
|---|---|
| #26030192 | 2 |
| #26028274 | 2 |
| #26020329 | 2 |
| #26018782 | 2 |
| #26018781 | 2 |
| #26018161 | 2 |
| C89×#3094 | 2 |
| #9983 | 89 |