Finite Group DatabasebetaFinite Group DatabasebetaOrder 22912.
216 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 216 conjugacy classes of subgroups — too many to draw. Only its 71 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. #26038487 | C2 | semidirect |
| 4. C4×#15668243 | C2 | semidirect |
| 5. #26038210 | C2 | semidirect |
| 6. #26038199 | C2 | semidirect |
| 14. #19153032 | C4 | semidirect |
| 15. #19153030 | C4 | semidirect |
| 95. C179 | #1932 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26038487 | 2 |
| #26038456 | 2 |
| #26038423 | 2 |
| C4×#15668243 | 2 |
| #26038210 | 2 |
| #26038199 | 2 |
| C2×#104×C179 | 2 |
| #1932 | 179 |