Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
254 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 254 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. D8×#10623494 | C2 | semidirect |
| 2. #26018326 | C2 | semidirect |
| 3. #26018213 | C2 | semidirect |
| 4. #26018168 | C2 | semidirect |
| 24. D16×C89 | C8 | semidirect |
| 38. D8×C89 | C2×C8 | semidirect |
| 45. C16×C89 | C2×C8 | semidirect |
| 80. C89 | #12045 | semidirect |
| 94. D16 | #10623494 | semidirect |
| 108. D8 | C2×#10623494 | semidirect |
| 120. C16 | C2×#10623494 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D8×#10623494 | 2 |
| #26018326 | 2 |
| #26018213 | 2 |
| #26018168 | 2 |
| C4×D16×C89 | 2 |
| #12045 | 89 |