Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
426 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 426 conjugacy classes of subgroups — too many to draw. Only its 141 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. #26012163 | C2 | semidirect |
| 2. #26011839 | C2 | semidirect |
| 3. #26011768 | C2 | semidirect |
| 4. #26011686 | C2 | semidirect |
| 5. Q8×#13063436 | C2 | semidirect |
| 6. C4×#14583811 | C2 | semidirect |
| 7. D4×Q8×C173 | C2 | semidirect |
| 55. Q8×C173 | D8 | semidirect |
| 57. D4×C173 | #41 | semidirect |
| 81. C173 | #3358 | semidirect |
| 84. D4×Q8 | D173 | semidirect |
| 129. Q8 | #14583811 | semidirect |
| 135. D4 | #14583827 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26012163 | 2 |
| #26011839 | 2 |
| #26011768 | 2 |
| #26011686 | 2 |
| Q8×#13063436 | 2 |
| C4×#14583811 | 2 |
| D4×Q8×C173 | 2 |
| #3358 | 173 |