Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
454 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 454 conjugacy classes of subgroups — too many to draw. Only its 131 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 |
|---|---|---|
| 2. #26018198 | C2 | semidirect |
| 3. #26018196 | C2 | semidirect |
| 24. #117×C89 | C8 | semidirect |
| 72. C42×C89 | C2×C8 | semidirect |
| 73. C42×C89 | C2×C8 | semidirect |
| 136. C89 | #11448 | semidirect |
| 154. #117 | #10623494 | semidirect |
| 204. C42 | C2×#10623494 | semidirect |
| 205. C42 | C2×#10623494 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19151324 | 2 |
| #26018198 | 2 |
| #26018196 | 2 |
| C89×#2317 | 2 |
| #11448 | 89 |