Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
456 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 145 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. #26012041 | C2 | semidirect |
| 2. #26011894 | C2 | semidirect |
| 3. #26011867 | C2 | semidirect |
| 4. #26011839 | C2 | semidirect |
| 5. #26011837 | C2 | semidirect |
| 6. #26011725 | C2 | semidirect |
| 7. C4×#14583811 | C2 | semidirect |
| 8. C2×C4×#13063436 | C2 | semidirect |
| 9. #532×C173 | C2 | semidirect |
| 77. #13063436 | #41 | semidirect |
| 89. C2×C4×C173 | D8 | semidirect |
| 120. C173 | #3169 | semidirect |
| 123. #532 | D173 | semidirect |
| 208. C2×C4 | #14583811 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26012041 | 2 |
| #26011894 | 2 |
| #26011867 | 2 |
| #26011839 | 2 |
| #26011837 | 2 |
| #26011725 | 2 |
| C4×#14583811 | 2 |
| C2×C4×#13063436 | 2 |
| #532×C173 | 2 |
| #3169 | 173 |