Finite Group DatabasebetaFinite Group DatabasebetaOrder 18112.
218 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 218 conjugacy classes of subgroups — too many to draw. Only its 95 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. #22583600 | C2 | semidirect |
| 3. #22583595 | C2 | semidirect |
| 4. #22583593 | C2 | semidirect |
| 5. #22583589 | C2 | semidirect |
| 6. #22583588 | C2 | semidirect |
| 8. C4×C22⋊D283 | C2 | semidirect |
| 9. C2×C4⋊C4×C283 | C2 | semidirect |
| 66. C283 | #539 | semidirect |
| 76. 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 |
| #22583600 | 2 |
| #22583595 | 2 |
| #22583593 | 2 |
| #22583589 | 2 |
| #22583588 | 2 |
| #22583584 | 2 |
| C4×C22⋊D283 | 2 |
| C2×C4⋊C4×C283 | 2 |
| #539 | 283 |