Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
544 conjugacy classes of subgroups; only the 94 normal subgroups are shown.
This group has 544 conjugacy classes of subgroups — too many to draw. Only its 94 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. #22626123 | C2 | semidirect |
| 3. #22625444 | C2 | semidirect |
| 5. #22624801 | C2 | semidirect |
| 6. #22624776 | C2 | semidirect |
| 93. #11924037 | SD16 | semidirect |
| 246. C73 | #9247 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D4×#11924037 | 2 |
| #22626123 | 2 |
| #22625444 | 2 |
| #22625256 | 2 |
| #22624801 | 2 |
| #22624776 | 2 |
| C2×#17988790 | 2 |
| #9247 | 73 |