Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
584 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 584 conjugacy classes of subgroups — too many to draw. Only its 157 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×#19149704 | C2 | semidirect |
| 2. C2×#19149676 | C2 | semidirect |
| 3. #26011691 | C2 | semidirect |
| 4. #26011686 | C2 | semidirect |
| 5. #26011515 | C2 | semidirect |
| 6. #26011495 | C2 | semidirect |
| 7. C4×#41×C173 | C2 | semidirect |
| 11. C2×#14583813 | C22 | semidirect |
| 12. C2×#14583811 | C22 | semidirect |
| 17. C4⋊#13063436 | C22 | semidirect |
| 18. #19149599 | C22 | semidirect |
| 20. C4×Q8×C173 | C22 | semidirect |
| 22. C4×D4×C173 | C22 | semidirect |
| 40. #41×C173 | D4 | semidirect |
| 69. Q8×C173 | C2×D4 | semidirect |
| 72. D4×C173 | C2×D4 | semidirect |
| 96. C4×C173 | AGL(1,ℤ/8) | semidirect |
| 104. C173 | #3038 | semidirect |
| 108. C4×#41 | D173 | semidirect |
| 123. C4×Q8 | C2×D173 | semidirect |
| 125. C4×D4 | C2×D173 | semidirect |
| 134. #41 | D692 | semidirect |
| 168. Q8 | C2×D692 | semidirect |
| 176. D4 | C2×D692 | semidirect |
| 201. C4 | #19149704 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19149704 | 2 |
| C2×#19149676 | 2 |
| #26011691 | 2 |
| #26011686 | 2 |
| #26011515 | 2 |
| #26011495 | 2 |
| C4×#41×C173 | 2 |
| #3038 | 173 |