Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
366 conjugacy classes of subgroups; only the 128 normal subgroups are shown.
This group has 366 conjugacy classes of subgroups — too many to draw. Only its 128 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 |
|---|---|---|
| 10. #17989514 | C4 | semidirect |
| 11. C16×#64408 | C4 | semidirect |
| 15. #17988415 | C4 | semidirect |
| 16. #17988414 | C4 | semidirect |
| 17. #367×C73 | C4 | semidirect |
| 60. #11924003 | C42 | semidirect |
| 63. C16×C73 | C42 | semidirect |
| 94. #64408 | #367 | direct (N × H) |
| 112. C73 | C4×#367 | semidirect |
| 122. #367 | #64408 | direct (N × H) |
| 170. C16 | C4×#64408 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17989514 | 2 |
| C2×C16×#64408 | 2 |
| #107×#64408 | 2 |
| #22624988 | 2 |
| #367×D73 | 2 |
| C4×#367 | 73 |