Finite Group DatabasebetaFinite Group DatabasebetaOrder 22912.
220 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 220 conjugacy classes of subgroups — too many to draw. Only its 61 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. #26038835 | C2 | semidirect |
| 3. #26038811 | C2 | semidirect |
| 4. #26038787 | C2 | semidirect |
| 5. #26038786 | C2 | semidirect |
| 6. #26038161 | C2 | semidirect |
| 7. #492×C179 | C2 | semidirect |
| 47. C179⋊C8 | SD16 | semidirect |
| 75. C179 | #1715 | semidirect |
| 80. #492 | D179 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26038835 | 2 |
| #26038815 | 2 |
| #26038811 | 2 |
| #26038787 | 2 |
| #26038786 | 2 |
| #26038161 | 2 |
| #492×C179 | 2 |
| #1715 | 179 |