Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
724 conjugacy classes of subgroups; only the 136 normal subgroups are shown.
This group has 724 conjugacy classes of subgroups — too many to draw. Only its 136 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 |
|---|---|---|
| 1. C4×#14556648 | C2 | semidirect |
| 3. #22625107 | C2 | semidirect |
| 4. #22624804 | C2 | semidirect |
| 12. #17989439 | C4 | semidirect |
| 15. C2×C4×D292 | C4 | semidirect |
| 17. #17988488 | C4 | semidirect |
| 18. #17988486 | C4 | semidirect |
| 23. C4×C4⋊C4×C73 | C4 | semidirect |
| 27. #14556648 | C2×C4 | semidirect |
| 32. (C2×#64408)⋊C4 | C2×C4 | semidirect |
| 234. C73 | #8220 | semidirect |
| 246. C4×C4⋊C4 | #64408 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#14556648 | 2 |
| C2×#17989439 | 2 |
| #22625107 | 2 |
| #22624804 | 2 |
| C4×#14556566 | 2 |
| #8220 | 73 |