Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
680 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 680 conjugacy classes of subgroups — too many to draw. Only its 90 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. #22625792 | C2 | semidirect |
| 3. #22625025 | C2 | semidirect |
| 11. C2×C4×D292 | C4 | semidirect |
| 14. #17988489 | C4 | semidirect |
| 16. #17988457 | C4 | semidirect |
| 17. C43×C73 | C4 | semidirect |
| 63. C2×D292 | C4⋊C4 | semidirect |
| 93. C42×C73 | C4⋊C4 | semidirect |
| 163. C4×C73 | #353 | semidirect |
| 179. C73 | #12797 | semidirect |
| 190. C43 | #64408 | semidirect |
| 268. C42 | C4⋊#64408 | semidirect |
| 340. C4 | #17989492 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17989492 | 2 |
| #22625792 | 2 |
| #22625025 | 2 |
| C4×#14556588 | 2 |
| #12797 | 73 |