Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
332 conjugacy classes of subgroups; only the 92 normal subgroups are shown.
This group has 332 conjugacy classes of subgroups — too many to draw. Only its 92 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×C22⋊#13063443 | C2 | semidirect |
| 2. #26012336 | C2 | semidirect |
| 3. #26012334 | C2 | semidirect |
| 38. C2×D4×C173 | C8 | semidirect |
| 62. C23×C173 | C2×C8 | semidirect |
| 68. C2×C4×C173 | C2×C8 | semidirect |
| 97. C173 | #1459 | semidirect |
| 119. C2×D4 | #13063443 | semidirect |
| 146. C23 | C2×#13063443 | semidirect |
| 165. C2×C4 | C2×#13063443 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C22⋊#13063443 | 2 |
| #26012336 | 2 |
| #26012334 | 2 |
| C2×D4×Dic173 | 2 |
| #1459 | 173 |