Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
726 conjugacy classes of subgroups; only the 200 normal subgroups are shown.
This group has 726 conjugacy classes of subgroups — too many to draw. Only its 200 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⋊#131 | C2 | semidirect |
| 2. #26012560 | C2 | semidirect |
| 3. #26012484 | C2 | semidirect |
| 4. #26012482 | C2 | semidirect |
| 5. #26012481 | C2 | semidirect |
| 6. C2×#19149742 | C2 | semidirect |
| 22. #19149727 | C4 | semidirect |
| 24. #19149726 | C4 | semidirect |
| 25. #19149726 | C4 | semidirect |
| 31. 2−1+4×C173 | C4 | semidirect |
| 45. #14583827 | C2×C4 | semidirect |
| 51. #14583826 | C2×C4 | semidirect |
| 55. #14583825 | C2×C4 | semidirect |
| 59. C2×Dic346 | C2×C4 | semidirect |
| 64. Q8×D173 | C2×C4 | semidirect |
| 75. #41×C173 | C2×C4 | semidirect |
| 77. C2×Q8×C173 | C2×C4 | semidirect |
| 141. C173 | #2898 | semidirect |
| 155. 2−1+4 | #10621924 | semidirect |
| 189. #41 | C2×#10621924 | semidirect |
| 201. C2×Q8 | C2×#10621924 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D173⋊#131 | 2 |
| #26012560 | 2 |
| #26012484 | 2 |
| #26012482 | 2 |
| #26012481 | 2 |
| C2×#19149742 | 2 |
| 2−1+4×D173 | 2 |
| #2898 | 173 |