Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
296 conjugacy classes of subgroups; only the 68 normal subgroups are shown.
This group has 296 conjugacy classes of subgroups — too many to draw. Only its 68 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. D173⋊#108 | C2 | semidirect |
| 2. #26012484 | C2 | semidirect |
| 4. D173⋊#101 | C2 | semidirect |
| 6. #26012454 | C2 | semidirect |
| 22. C2×#14583815 | C4 | semidirect |
| 23. C2×#14583814 | C4 | semidirect |
| 24. C2×#14583813 | C4 | semidirect |
| 30. C2×SD16×C173 | C4 | semidirect |
| 133. C173 | #1977 | semidirect |
| 151. C2×SD16 | #10621924 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D173⋊#108 | 2 |
| #26012484 | 2 |
| #26012483 | 2 |
| D173⋊#101 | 2 |
| D173⋊#100 | 2 |
| #26012454 | 2 |
| C2×SD16×D173 | 2 |
| #1977 | 173 |