Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
368 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 368 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 |
|---|---|---|
| 2. #26011894 | C2 | semidirect |
| 3. #26011870 | C2 | semidirect |
| 4. #26011843 | C2 | semidirect |
| 5. #26011841 | C2 | semidirect |
| 7. C4×#14583816 | C2 | semidirect |
| 79. C2×C4×C173 | Q16 | semidirect |
| 104. C173 | #3170 | semidirect |
| 182. C2×C4 | #14583816 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26012048 | 2 |
| #26011894 | 2 |
| #26011870 | 2 |
| #26011843 | 2 |
| #26011841 | 2 |
| #26011730 | 2 |
| C4×#14583816 | 2 |
| C2×C4×#13063436 | 2 |
| #533×C173 | 2 |
| #3170 | 173 |