Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
444 conjugacy classes of subgroups; only the 88 normal subgroups are shown.
This group has 444 conjugacy classes of subgroups — too many to draw. Only its 88 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 |
|---|---|---|
| 3. #22624903 | C2 | direct (N × H) |
| 15. #17988842 | C4 | semidirect |
| 17. C2×#14556523 | C4 | semidirect |
| 19. C22×Q16×C73 | C4 | semidirect |
| 46. #14556523 | C2×C4 | semidirect |
| 53. C2×Q16×C73 | C2×C4 | semidirect |
| 163. C2×C73 | #1340 | semidirect |
| 171. C73 | C2×#1340 | semidirect |
| 172. C22×Q16 | #64408 | semidirect |
| 192. C2×Q16 | C2×#64408 | semidirect |
| 331. C2 | #22624903 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17989484 | 2 |
| C2×#17989455 | 2 |
| #22624903 | 2 |
| C2×#17988842 | 2 |
| C2×#1340 | 73 |