Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
162 conjugacy classes of subgroups; only the 64 normal subgroups are shown.
This group has 162 conjugacy classes of subgroups — too many to draw. Only its 64 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×#19149754 | C2 | semidirect |
| 2. C2×#19149753 | C2 | semidirect |
| 3. #26012412 | C2 | semidirect |
| 4. #26012386 | C2 | semidirect |
| 5. C22⋊#14583829 | C2 | semidirect |
| 6. #26012377 | C2 | semidirect |
| 24. #14583829 | D4 | semidirect |
| 69. Dic173 | M32 | semidirect |
| 75. C173 | #2169 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19149754 | 2 |
| C2×#19149753 | 2 |
| #26012412 | 2 |
| #26012386 | 2 |
| C22⋊#14583829 | 2 |
| #26012377 | 2 |
| #26011554 | 2 |
| #2169 | 173 |