Finite Group DatabasebetaFinite Group DatabasebetaOrder 22912.
154 conjugacy classes of subgroups; only the 45 normal subgroups are shown.
This group has 154 conjugacy classes of subgroups — too many to draw. Only its 45 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. #26038879 | C2 | semidirect |
| 2. #26038822 | C2 | semidirect |
| 3. #26038556 | C2 | semidirect |
| 4. #26038259 | C2 | semidirect |
| 5. #26038256 | C2 | semidirect |
| 6. #26038252 | C2 | semidirect |
| 74. C179 | #2212 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26038879 | 2 |
| #26038822 | 2 |
| #26038556 | 2 |
| #26038259 | 2 |
| #26038256 | 2 |
| #26038252 | 2 |
| #509×C179 | 2 |
| #2212 | 179 |