Finite Group DatabasebetaFinite Group DatabasebetaOrder 18112.
214 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 214 conjugacy classes of subgroups — too many to draw. Only its 99 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. #22583605 | C2 | semidirect |
| 2. #22583601 | C2 | semidirect |
| 3. #22583600 | C2 | semidirect |
| 5. #22583590 | C2 | semidirect |
| 6. #22583589 | C2 | semidirect |
| 7. #22583575 | C2 | semidirect |
| 9. #22583569 | C2 | semidirect |
| 10. #22583568 | C2 | semidirect |
| 11. C2×C4⋊C4×C283 | C2 | semidirect |
| 72. C283 | #552 | semidirect |
| 84. C2×C4⋊C4 | D283 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22583605 | 2 |
| #22583601 | 2 |
| #22583600 | 2 |
| #22583593 | 2 |
| #22583590 | 2 |
| #22583589 | 2 |
| #22583575 | 2 |
| C4×C22⋊D283 | 2 |
| #22583569 | 2 |
| #22583568 | 2 |
| C2×C4⋊C4×C283 | 2 |
| #552 | 283 |