Finite Group DatabasebetaFinite Group DatabasebetaOrder 18112.
270 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 270 conjugacy classes of subgroups — too many to draw. Only its 103 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 |
|---|---|---|
| 2. C2×Q8×D283 | C2 | semidirect |
| 3. #22583609 | C2 | semidirect |
| 4. #22583596 | C2 | semidirect |
| 5. #22583595 | C2 | semidirect |
| 6. #22583592 | C2 | semidirect |
| 7. #22583590 | C2 | semidirect |
| 8. #22583589 | C2 | semidirect |
| 9. #22583586 | C2 | semidirect |
| 10. #22583568 | C2 | semidirect |
| 11. C22⋊Q8×C283 | C2 | semidirect |
| 83. C283 | #536 | semidirect |
| 94. C22⋊Q8 | D283 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17985392 | 2 |
| C2×Q8×D283 | 2 |
| #22583609 | 2 |
| #22583596 | 2 |
| #22583595 | 2 |
| #22583592 | 2 |
| #22583590 | 2 |
| #22583589 | 2 |
| #22583586 | 2 |
| #22583568 | 2 |
| C22⋊Q8×C283 | 2 |
| #536 | 283 |