Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
408 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 408 conjugacy classes of subgroups — too many to draw. Only its 113 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×#17988409 | C2 | semidirect |
| 4. #22610667 | C2 | semidirect |
| 5. #22608040 | C2 | semidirect |
| 6. #22608010 | C2 | semidirect |
| 18. #17988391 | C4 | semidirect |
| 19. #17988388 | C4 | semidirect |
| 87. Q16×C73 | C4⋊C4 | semidirect |
| 91. D8×C73 | C4⋊C4 | semidirect |
| 163. C73 | #12955 | semidirect |
| 229. Q16 | #11924007 | semidirect |
| 233. D8 | #11924007 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17988709 | 2 |
| C2×#17988409 | 2 |
| #22611643 | 2 |
| #22610667 | 2 |
| #22608040 | 2 |
| #22608010 | 2 |
| C2×#360×C73 | 2 |
| #12955 | 73 |