Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
360 conjugacy classes of subgroups; only the 92 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 92 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 |
|---|---|---|
| 3. M16×#10621924 | C2 | semidirect |
| 4. C42×#10621924 | C2 | semidirect |
| 5. #26012363 | C2 | semidirect |
| 6. #26012362 | C2 | semidirect |
| 9. Q8×#10621924 | C4 | semidirect |
| 11. D4×#10621924 | C4 | semidirect |
| 18. #19149744 | C4 | semidirect |
| 19. #19149743 | C4 | semidirect |
| 25. #19149607 | C4 | semidirect |
| 26. #19149606 | C4 | semidirect |
| 27. #19149605 | C4 | semidirect |
| 28. #104×C173 | C4 | semidirect |
| 32. #14583836 | C2×C4 | semidirect |
| 44. C4×#10621924 | C2×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 | C42 | semidirect |
| 79. D692 | C42 | semidirect |
| 95. Q8×C173 | C42 | semidirect |
| 97. D4×C173 | C42 | semidirect |
| 112. #10621924 | #104 | direct (N × H) |
| 127. C173 | C4×#104 | semidirect |
| 154. #104 | #10621924 | direct (N × H) |
| 176. M16 | C2×#10621924 | semidirect |
| 193. C42 | C2×#10621924 | semidirect |
| 198. Q8 | C4×#10621924 | semidirect |
| 205. D4 | C4×#10621924 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #41×#10621924 | 2 |
| D173⋊#104 | 2 |
| M16×#10621924 | 2 |
| C42×#10621924 | 2 |
| #26012363 | 2 |
| #26012362 | 2 |
| #104×D173 | 2 |
| C4×#104 | 173 |