Finite Group DatabasebetaFinite Group DatabasebetaOrder 22912.
216 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 216 conjugacy classes of subgroups — too many to draw. Only its 73 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. #26038463 | C2 | semidirect |
| 3. #26038171 | C2 | semidirect |
| 4. #26038168 | C2 | semidirect |
| 5. #431×C179 | C2 | semidirect |
| 93. C179 | #1495 | semidirect |
| 96. #431 | D179 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26038973 | 2 |
| #26038463 | 2 |
| #26038171 | 2 |
| #26038168 | 2 |
| #431×C179 | 2 |
| #1495 | 179 |