Finite Group DatabasebetaFinite Group DatabasebetaOrder 36224.
336 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 336 conjugacy classes of subgroups — too many to draw. Only its 57 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. #31827100 | C2 | semidirect |
| 2. #31826657 | C2 | semidirect |
| 3. #31826209 | C2 | semidirect |
| 4. #31826194 | C2 | semidirect |
| 5. #493×C283 | C2 | semidirect |
| 11. C4⋊(C283⋊C8) | C22 | semidirect |
| 15. #127×C283 | C22 | semidirect |
| 16. C4×C8×C283 | C22 | semidirect |
| 39. D1132 | D8 | semidirect |
| 74. C283 | #1619 | semidirect |
| 77. #493 | D283 | semidirect |
| 85. #127 | C2×D283 | semidirect |
| 91. C4×C8 | C2×D283 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31827100 | 2 |
| #31826657 | 2 |
| #31826209 | 2 |
| #31826194 | 2 |
| #493×C283 | 2 |
| #1619 | 283 |