Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
402 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 402 conjugacy classes of subgroups — too many to draw. Only its 133 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. #26012048 | C2 | semidirect |
| 3. #26011896 | C2 | semidirect |
| 4. #26011864 | C2 | semidirect |
| 5. #26011842 | C2 | semidirect |
| 6. #26011838 | C2 | semidirect |
| 7. #26011737 | C2 | semidirect |
| 8. #26011593 | C2 | semidirect |
| 9. C4×M16×C173 | C2 | semidirect |
| 90. C8×C173 | #41 | semidirect |
| 112. C173 | #3182 | semidirect |
| 122. C4×M16 | D173 | semidirect |
| 203. C8 | #14583826 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26012048 | 2 |
| #26012041 | 2 |
| #26011896 | 2 |
| #26011864 | 2 |
| #26011842 | 2 |
| #26011838 | 2 |
| #26011737 | 2 |
| #26011593 | 2 |
| C4×M16×C173 | 2 |
| #3182 | 173 |