Finite Group DatabasebetaFinite Group DatabasebetaOrder 22336.
268 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 268 conjugacy classes of subgroups — too many to draw. Only its 107 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. #26013685 | C2 | semidirect |
| 2. #26013665 | C2 | semidirect |
| 3. #26013664 | C2 | semidirect |
| 4. #26013659 | C2 | semidirect |
| 5. C2×#19150218 | C2 | semidirect |
| 6. #26013646 | C2 | semidirect |
| 7. H(5,𝔽2)×C349 | C2 | semidirect |
| 9. #19150233 | C22 | semidirect |
| 10. C2×D1396 | C22 | semidirect |
| 12. #19150223 | C22 | semidirect |
| 13. #19150221 | C22 | semidirect |
| 14. #19150220 | C22 | semidirect |
| 15. #19150218 | C22 | semidirect |
| 16. #19150218 | C22 | semidirect |
| 17. #19150217 | C22 | semidirect |
| 18. C2×#14584095 | C22 | semidirect |
| 21. #41×C349 | C22 | semidirect |
| 23. C2×D4×C349 | C22 | semidirect |
| 54. C349 | #576 | semidirect |
| 57. H(5,𝔽2) | D349 | semidirect |
| 67. #41 | C2×D349 | semidirect |
| 71. C2×D4 | C2×D349 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26013685 | 2 |
| #26013665 | 2 |
| #26013664 | 2 |
| #26013659 | 2 |
| C2×#19150218 | 2 |
| #26013646 | 2 |
| H(5,𝔽2)×C349 | 2 |
| #576 | 349 |