Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
500 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 500 conjugacy classes of subgroups — too many to draw. Only its 109 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. C2×#19151645 | C2 | semidirect |
| 3. #26021981 | C2 | semidirect |
| 4. #26021979 | C2 | semidirect |
| 5. C2×#19151379 | C2 | semidirect |
| 6. #26018368 | C2 | semidirect |
| 7. C89×#1389 | C2 | semidirect |
| 57. #15667948 | D4 | semidirect |
| 68. #108×C89 | D4 | semidirect |
| 191. #1389 | D89 | semidirect |
| 192. C89 | #12998 | semidirect |
| 251. #108 | D356 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26029862 | 2 |
| C2×#19151645 | 2 |
| #26021981 | 2 |
| #26021979 | 2 |
| C2×#19151379 | 2 |
| #26018368 | 2 |
| C89×#1389 | 2 |
| #12998 | 89 |