Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
418 conjugacy classes of subgroups; only the 192 normal subgroups are shown.
This group has 418 conjugacy classes of subgroups — too many to draw. Only its 192 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. #17989477 | C4 | direct (N × H) |
| 11. #17989476 | C4 | semidirect |
| 12. C4×#11924031 | C4 | semidirect |
| 15. #17988362 | C4 | semidirect |
| 16. C4×#11924003 | C4 | semidirect |
| 17. C4×C16×C73 | C4 | semidirect |
| 43. #11924031 | C42 | semidirect |
| 52. #11924003 | C42 | semidirect |
| 56. C16×C73 | C42 | semidirect |
| 76. C4×C73 | #347 | semidirect |
| 89. C73 | C4×#347 | semidirect |
| 102. C4×C16 | #64408 | semidirect |
| 141. C16 | C4×#64408 | semidirect |
| 163. C4 | #17989477 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17989477 | 2 |
| C4×#14556666 | 2 |
| C4×#14556645 | 2 |
| C4×#14556530 | 2 |
| C4×#347 | 73 |