Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
372 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 372 conjugacy classes of subgroups — too many to draw. Only its 117 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. #26012215 | C2 | semidirect |
| 2. D4×Dic346 | C2 | semidirect |
| 3. #26011852 | C2 | semidirect |
| 4. #26011841 | C2 | semidirect |
| 5. #26011784 | C2 | semidirect |
| 6. #26011772 | C2 | semidirect |
| 8. #26011618 | C2 | semidirect |
| 9. #26011592 | C2 | semidirect |
| 11. #461×C173 | C2 | semidirect |
| 122. C173 | #3367 | semidirect |
| 131. #461 | D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26012215 | 2 |
| D4×Dic346 | 2 |
| #26011852 | 2 |
| #26011841 | 2 |
| #26011784 | 2 |
| #26011772 | 2 |
| #26011708 | 2 |
| #26011618 | 2 |
| #26011592 | 2 |
| C4×#14583811 | 2 |
| #461×C173 | 2 |
| #3367 | 173 |