Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
184 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 184 conjugacy classes of subgroups — too many to draw. Only its 78 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. #26012355 | C2 | semidirect |
| 3. #26012354 | C2 | semidirect |
| 39. #13063436 | M16 | semidirect |
| 46. C8×C173 | M16 | semidirect |
| 63. C173 | #1567 | semidirect |
| 110. C8 | #14583835 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26012494 | 2 |
| #26012355 | 2 |
| #26012354 | 2 |
| C2×C8×Dic173 | 2 |
| #1567 | 173 |