Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
430 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 430 conjugacy classes of subgroups — too many to draw. Only its 141 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. #17989677 | C4 | semidirect |
| 12. #17989671 | C4 | semidirect |
| 32. #14556659 | C8 | semidirect |
| 38. #14556523 | C8 | semidirect |
| 39. #14556522 | C8 | semidirect |
| 40. #106×C73 | C8 | semidirect |
| 97. C8×C73 | C4×C8 | semidirect |
| 98. #10596831 | C4×C8 | semidirect |
| 127. C73 | #8285 | semidirect |
| 152. #106 | #10596842 | semidirect |
| 220. C8 | C4×#10596842 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4⋊C4×#10596842 | 2 |
| C2×#17989677 | 2 |
| C2×#17989671 | 2 |
| #22626939 | 2 |
| #106×#64408 | 2 |
| #8285 | 73 |