Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
654 conjugacy classes of subgroups; only the 308 normal subgroups are shown.
This group has 654 conjugacy classes of subgroups — too many to draw. Only its 308 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 |
|---|---|---|
| 11. #17989429 | C4 | semidirect |
| 12. #17989428 | C4 | semidirect |
| 15. #17988309 | C4 | semidirect |
| 16. #17988308 | C4 | semidirect |
| 17. #322×C73 | C4 | semidirect |
| 26. C8×#64408 | C8 | semidirect |
| 64. #10596833 | C4×C8 | semidirect |
| 66. C8×C73 | C4×C8 | semidirect |
| 68. #10596831 | C4×C8 | semidirect |
| 72. #64408 | #322 | direct (N × H) |
| 86. C73 | C4×#322 | semidirect |
| 98. #322 | #64408 | direct (N × H) |
| 149. C8 | C8×#64408 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×C8×#64408 | 2 |
| #22625127 | 2 |
| #22625125 | 2 |
| #322×D73 | 2 |
| C4×#322 | 73 |