Finite Group DatabasebetaFinite Group DatabasebetaOrder 22592.
298 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 298 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. C22×D1412 | C2 | semidirect |
| 2. #26015017 | C2 | direct (N × H) |
| 3. C2×#19150724 | C2 | semidirect |
| 4. C2×#19150722 | C2 | semidirect |
| 5. C2×#19150721 | C2 | semidirect |
| 6. C2×#41×C353 | C2 | semidirect |
| 11. C2×D1412 | C22 | semidirect |
| 12. #19150724 | C22 | semidirect |
| 13. #19150722 | C22 | semidirect |
| 14. #19150721 | C22 | semidirect |
| 15. C2×#15667725 | C22 | semidirect |
| 17. #41×C353 | C22 | semidirect |
| 18. C2×Q8×C353 | C22 | semidirect |
| 20. C2×D4×C353 | C22 | semidirect |
| 29. #15667725 | C23 | semidirect |
| 33. Q8×C353 | C23 | semidirect |
| 36. D4×C353 | C23 | semidirect |
| 57. C2×C353 | AGL(1,ℤ/8) | semidirect |
| 60. C353 | C2×AGL(1,ℤ/8) | semidirect |
| 62. C2×#41 | D353 | semidirect |
| 70. #41 | C2×D353 | semidirect |
| 71. C2×Q8 | C2×D353 | semidirect |
| 77. C2×D4 | C2×D353 | semidirect |
| 90. Q8 | C22×D353 | semidirect |
| 96. D4 | C22×D353 | semidirect |
| 119. C2 | #26015017 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D1412 | 2 |
| #26015017 | 2 |
| C2×#19150724 | 2 |
| C2×#19150722 | 2 |
| C2×#19150721 | 2 |
| C2×#41×C353 | 2 |
| C2×AGL(1,ℤ/8) | 353 |