Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
332 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 332 conjugacy classes of subgroups — too many to draw. Only its 79 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. C4×#14583826 | C2 | semidirect |
| 3. #26011509 | C2 | semidirect |
| 4. C2×#19149607 | C2 | semidirect |
| 5. #26011464 | C2 | semidirect |
| 6. #26011263 | C2 | semidirect |
| 7. #339×C173 | C2 | semidirect |
| 11. #19149712 | C4 | semidirect |
| 13. #19149707 | C4 | semidirect |
| 37. C2×Dic346 | C2×C4 | semidirect |
| 39. C2×D692 | C2×C4 | semidirect |
| 62. M16×C173 | C2×C4 | semidirect |
| 129. C173 | #1906 | semidirect |
| 137. #339 | D173 | semidirect |
| 185. M16 | C4×D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26012291 | 2 |
| C4×#14583826 | 2 |
| #26011509 | 2 |
| C2×#19149607 | 2 |
| #26011464 | 2 |
| #26011263 | 2 |
| #339×C173 | 2 |
| #1906 | 173 |