Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
648 conjugacy classes of subgroups; only the 181 normal subgroups are shown.
This group has 648 conjugacy classes of subgroups — too many to draw. Only its 181 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. C22×#14583811 | C2 | semidirect |
| 2. C2×#19149676 | C2 | semidirect |
| 3. #26011686 | C2 | direct (N × H) |
| 4. C2×C4⋊#13063436 | C2 | semidirect |
| 5. C2×#19149599 | C2 | semidirect |
| 6. C2×C4×D4×C173 | C2 | semidirect |
| 11. C2×#14583811 | C22 | semidirect |
| 14. #19149676 | C22 | semidirect |
| 15. C4⋊#13063436 | C22 | semidirect |
| 16. #19149599 | C22 | semidirect |
| 20. C4×D4×C173 | C22 | semidirect |
| 39. C2×D4×C173 | D4 | semidirect |
| 69. D4×C173 | C2×D4 | semidirect |
| 74. C2×C4×C173 | D8 | semidirect |
| 96. C4×C173 | C2×D8 | semidirect |
| 100. C2×C173 | #459 | semidirect |
| 105. C173 | C2×#459 | semidirect |
| 109. C2×C4×D4 | D173 | semidirect |
| 124. C4×D4 | C2×D173 | semidirect |
| 142. C2×D4 | D692 | semidirect |
| 174. D4 | C2×D692 | semidirect |
| 179. C2×C4 | #14583811 | semidirect |
| 202. C4 | C2×#14583811 | semidirect |
| 207. C2 | #26011686 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14583811 | 2 |
| C2×#19149676 | 2 |
| #26011686 | 2 |
| C2×C4⋊#13063436 | 2 |
| C2×#19149599 | 2 |
| C2×C4×D4×C173 | 2 |
| C2×#459 | 173 |