Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
1060 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 1060 conjugacy classes of subgroups — too many to draw. Only its 105 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. C2×#19151731 | C2 | semidirect |
| 2. #26023890 | C2 | semidirect |
| 3. #26021089 | C2 | semidirect |
| 4. #26020184 | C2 | semidirect |
| 5. #26018820 | C2 | semidirect |
| 6. #26018099 | C2 | semidirect |
| 7. C89×#3186 | C2 | semidirect |
| 55. C22⋊#10623494 | D4 | semidirect |
| 61. C22×D4×C89 | D4 | semidirect |
| 64. C22×C8×C89 | D4 | semidirect |
| 74. C2×C4⋊C4×C89 | D4 | semidirect |
| 113. C22⋊Dic89 | D8 | semidirect |
| 269. #3186 | D89 | semidirect |
| 276. C89 | #9946 | semidirect |
| 312. C22×D4 | C22⋊D89 | semidirect |
| 318. C22×C8 | C22⋊D89 | semidirect |
| 332. C2×C4⋊C4 | C22⋊D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19151731 | 2 |
| #26023890 | 2 |
| #26021089 | 2 |
| #26020184 | 2 |
| #26018820 | 2 |
| #26018099 | 2 |
| C89×#3186 | 2 |
| #9946 | 89 |