Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
686 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 686 conjugacy classes of subgroups — too many to draw. Only its 99 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. #26030253 | C2 | semidirect |
| 2. #26029716 | C2 | semidirect |
| 3. #26025149 | C2 | semidirect |
| 4. #26018813 | C2 | semidirect |
| 5. #26018678 | C2 | semidirect |
| 6. #26018111 | C2 | semidirect |
| 7. C89×#1478 | C2 | semidirect |
| 43. #15668012 | D4 | semidirect |
| 44. #15668009 | D4 | semidirect |
| 63. C4⋊#10623494 | D4 | semidirect |
| 85. C4×C8×C89 | D4 | semidirect |
| 135. C2×D4×C89 | D8 | semidirect |
| 262. #1478 | D89 | semidirect |
| 264. C89 | #9996 | semidirect |
| 339. C4×C8 | C22⋊D89 | semidirect |
| 365. C2×D4 | D712 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26030253 | 2 |
| #26029716 | 2 |
| #26025149 | 2 |
| #26018813 | 2 |
| #26018678 | 2 |
| #26018111 | 2 |
| C89×#1478 | 2 |
| #9996 | 89 |