Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
478 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 478 conjugacy classes of subgroups — too many to draw. Only its 75 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. C2×#19149707 | C2 | semidirect |
| 2. #26012060 | C2 | semidirect |
| 3. C2×#19149676 | C2 | semidirect |
| 4. C2×#19149607 | C2 | semidirect |
| 5. #26011495 | C2 | semidirect |
| 6. C2×#19149595 | C2 | semidirect |
| 7. #339×C173 | C2 | semidirect |
| 35. C2×Dic346 | D4 | semidirect |
| 50. C2×D692 | D4 | semidirect |
| 51. C2×D692 | D4 | semidirect |
| 63. M16×C173 | D4 | semidirect |
| 65. C4⋊C4×C173 | D4 | semidirect |
| 69. C42×C173 | D4 | semidirect |
| 138. C173 | #2002 | semidirect |
| 146. #339 | D173 | semidirect |
| 200. M16 | D692 | semidirect |
| 203. C4⋊C4 | D692 | semidirect |
| 208. C42 | D692 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19149707 | 2 |
| #26012060 | 2 |
| C2×#19149676 | 2 |
| C2×#19149607 | 2 |
| #26011495 | 2 |
| C2×#19149595 | 2 |
| #339×C173 | 2 |
| #2002 | 173 |