Finite Group DatabasebetaFinite Group DatabasebetaOrder 22336.
338 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 338 conjugacy classes of subgroups — too many to draw. Only its 111 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×D4×D349 | C2 | semidirect |
| 2. C2×D2792 | C2 | semidirect |
| 3. C2×#19150218 | C2 | semidirect |
| 4. D8×D349 | C2 | direct (N × H) |
| 5. C2×C8×D349 | C2 | semidirect |
| 6. C2×D8×C349 | C2 | semidirect |
| 8. C2×D1396 | C22 | semidirect |
| 11. D4×D349 | C22 | semidirect |
| 13. D2792 | C22 | semidirect |
| 14. #19150218 | C22 | semidirect |
| 15. C2×#14584095 | C22 | semidirect |
| 16. C8×D349 | C22 | semidirect |
| 17. C2×D4×C349 | C22 | semidirect |
| 18. D8×C349 | C22 | semidirect |
| 19. C2×C8×C349 | C22 | semidirect |
| 25. D1396 | C23 | semidirect |
| 30. #14584095 | C23 | semidirect |
| 33. D4×C349 | C23 | semidirect |
| 35. C8×C349 | C23 | semidirect |
| 42. C2×D349 | D8 | direct (N × H) |
| 48. C2×C349 | C2×D8 | semidirect |
| 51. D349 | C2×D8 | direct (N × H) |
| 52. C349 | C22×D8 | semidirect |
| 58. C2×D8 | D349 | direct (N × H) |
| 65. C2×D4 | C2×D349 | semidirect |
| 69. D8 | C2×D349 | direct (N × H) |
| 72. C2×C8 | C2×D349 | semidirect |
| 82. D4 | C22×D349 | semidirect |
| 88. C8 | C22×D349 | semidirect |
| 103. C2 | D8×D349 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D4×D349 | 2 |
| C2×D2792 | 2 |
| C2×#19150218 | 2 |
| D8×D349 | 2 |
| C2×C8×D349 | 2 |
| C2×D8×C349 | 2 |
| C22×D8 | 349 |