Finite Group DatabasebetaFinite Group DatabasebetaOrder 36224.
368 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 368 conjugacy classes of subgroups — too many to draw. Only its 117 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×#22583629 | C2 | semidirect |
| 2. #31826894 | C2 | direct (N × H) |
| 3. C2×Dic2264 | C2 | semidirect |
| 4. C2×#22583554 | C2 | semidirect |
| 5. C2×C16×D283 | C2 | semidirect |
| 6. C2×D16×C283 | C2 | semidirect |
| 9. #22583629 | C22 | semidirect |
| 13. Dic2264 | C22 | semidirect |
| 14. #22583554 | C22 | semidirect |
| 16. C16×D283 | C22 | semidirect |
| 18. D16×C283 | C22 | semidirect |
| 64. C2×C283 | #508 | semidirect |
| 67. C283 | C2×#508 | semidirect |
| 73. C2×D16 | D283 | semidirect |
| 84. D16 | C2×D283 | semidirect |
| 133. C2 | #31826894 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22583629 | 2 |
| #31826894 | 2 |
| C2×Dic2264 | 2 |
| C2×#22583554 | 2 |
| C2×C16×D283 | 2 |
| C2×D16×C283 | 2 |
| C2×#508 | 283 |