Finite Group DatabasebetaFinite Group DatabasebetaOrder 22912.
162 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 162 conjugacy classes of subgroups — too many to draw. Only its 65 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. #26038569 | C2 | semidirect |
| 4. #26038192 | C2 | semidirect |
| 5. #26038171 | C2 | semidirect |
| 7. #322×C179 | C2 | semidirect |
| 60. C8×C179 | M16 | semidirect |
| 77. C179 | #1592 | semidirect |
| 85. #322 | D179 | semidirect |
| 138. C8 | #15668242 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26038569 | 2 |
| C4×#15668248 | 2 |
| #26038518 | 2 |
| #26038192 | 2 |
| #26038171 | 2 |
| #26038168 | 2 |
| #322×C179 | 2 |
| #1592 | 179 |