Finite Group DatabasebetaFinite Group DatabasebetaOrder 22912.
216 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 216 conjugacy classes of subgroups — too many to draw. Only its 69 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. C4×#15668243 | C2 | semidirect |
| 3. #26038180 | C2 | semidirect |
| 4. #26038178 | C2 | semidirect |
| 5. #432×C179 | C2 | semidirect |
| 90. C179 | #1529 | semidirect |
| 93. #432 | D179 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26038973 | 2 |
| C4×#15668243 | 2 |
| #26038180 | 2 |
| #26038178 | 2 |
| #432×C179 | 2 |
| #1529 | 179 |