Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
698 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 698 conjugacy classes of subgroups — too many to draw. Only its 113 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. #22627073 | C2 | semidirect |
| 2. #22627065 | C2 | semidirect |
| 3. C2×D4⋊#10596842 | C2 | semidirect |
| 21. C4×#10596842 | D4 | semidirect |
| 36. #14556588 | C8 | semidirect |
| 38. #14556587 | C8 | semidirect |
| 40. #127×C73 | C8 | semidirect |
| 145. C73 | #9642 | semidirect |
| 166. #127 | #10596842 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22627073 | 2 |
| #22627065 | 2 |
| C2×D4⋊#10596842 | 2 |
| #127×#64408 | 2 |
| #9642 | 73 |