Finite Group DatabasebetaFinite Group DatabasebetaOrder 22912.
208 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 208 conjugacy classes of subgroups — too many to draw. Only its 101 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 |
|---|---|---|
| 4. #26038161 | C2 | semidirect |
| 5. #26038161 | C2 | semidirect |
| 6. #26038161 | C2 | semidirect |
| 7. #322×C179 | C2 | semidirect |
| 45. C179⋊C8 | M16 | semidirect |
| 66. C179 | #1451 | semidirect |
| 74. #322 | D179 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26038490 | 2 |
| C4×#15668242 | 2 |
| C4×C8×D179 | 2 |
| #26038161 | 2 |
| #322×C179 | 2 |
| #1451 | 179 |