Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
584 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 584 conjugacy classes of subgroups — too many to draw. Only its 149 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×#19149705 | C2 | semidirect |
| 2. C4×#14583826 | C2 | semidirect |
| 3. #26011688 | C2 | semidirect |
| 4. #26011683 | C2 | semidirect |
| 5. #26011515 | C2 | semidirect |
| 6. #26011496 | C2 | semidirect |
| 7. C2×#127×C173 | C2 | semidirect |
| 10. C2×#14583814 | C22 | semidirect |
| 11. C2×#14583811 | C22 | semidirect |
| 13. C4×Dic346 | C22 | semidirect |
| 14. C4×D692 | C22 | semidirect |
| 19. C4⋊#13063436 | C22 | semidirect |
| 20. #19149600 | C22 | semidirect |
| 28. #14583826 | D4 | semidirect |
| 59. Dic346 | C2×D4 | semidirect |
| 61. D692 | C2×D4 | semidirect |
| 94. C4×C173 | AGL(1,ℤ/8) | semidirect |
| 104. C173 | #3038 | semidirect |
| 107. C2×#127 | D173 | semidirect |
| 201. C4 | #19149705 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19149705 | 2 |
| C4×#14583826 | 2 |
| #26011688 | 2 |
| #26011683 | 2 |
| #26011515 | 2 |
| #26011496 | 2 |
| C2×#127×C173 | 2 |
| #3038 | 173 |