Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
302 conjugacy classes of subgroups; only the 68 normal subgroups are shown.
This group has 302 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 |
|---|---|---|
| 2. #26012502 | C2 | semidirect |
| 4. #26012437 | C2 | semidirect |
| 5. #26012370 | C2 | semidirect |
| 6. #26012362 | C2 | semidirect |
| 25. #19149607 | C4 | semidirect |
| 26. #19149606 | C4 | semidirect |
| 27. #19149605 | C4 | semidirect |
| 28. #104×C173 | C4 | semidirect |
| 58. #14583810 | C2×C4 | semidirect |
| 62. C4×Dic173 | C2×C4 | semidirect |
| 64. M16×C173 | C2×C4 | semidirect |
| 65. C42×C173 | C2×C4 | semidirect |
| 77. Dic346 | C4⋊C4 | semidirect |
| 79. D692 | C4⋊C4 | semidirect |
| 96. Q8×C173 | C4⋊C4 | semidirect |
| 98. D4×C173 | C4⋊C4 | semidirect |
| 131. C173 | #1859 | semidirect |
| 158. #104 | #10621924 | semidirect |
| 180. M16 | C2×#10621924 | semidirect |
| 197. C42 | C2×#10621924 | semidirect |
| 202. Q8 | C4⋊#10621924 | semidirect |
| 209. D4 | C4⋊#10621924 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26012560 | 2 |
| #26012502 | 2 |
| #26012482 | 2 |
| #26012437 | 2 |
| #26012370 | 2 |
| #26012362 | 2 |
| #104×D173 | 2 |
| #1859 | 173 |