Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
576 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 576 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. #26030641 | C2 | semidirect |
| 3. #26018875 | C2 | semidirect |
| 4. #26018803 | C2 | semidirect |
| 5. #26018695 | C2 | semidirect |
| 6. #26018118 | C2 | semidirect |
| 7. C89×#3110 | C2 | semidirect |
| 53. C4×#10623494 | D4 | semidirect |
| 61. C4⋊Q8×C89 | D4 | semidirect |
| 62. C4⋊Q8×C89 | D4 | semidirect |
| 81. #97×C89 | D4 | semidirect |
| 212. #3110 | D89 | semidirect |
| 218. C89 | #10022 | semidirect |
| 251. C4⋊Q8 | C22⋊D89 | semidirect |
| 252. C4⋊Q8 | C22⋊D89 | semidirect |
| 287. #97 | C22⋊D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26030641 | 2 |
| #26026104 | 2 |
| #26018875 | 2 |
| #26018803 | 2 |
| #26018695 | 2 |
| #26018118 | 2 |
| C89×#3110 | 2 |
| #10022 | 89 |