Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
786 conjugacy classes of subgroups; only the 256 normal subgroups are shown.
This group has 786 conjugacy classes of subgroups — too many to draw. Only its 256 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 |
|---|---|---|
| 2. #22625986 | C2 | semidirect |
| 3. #22625858 | C2 | semidirect |
| 4. #22625723 | C2 | semidirect |
| 6. C42×#10596833 | C2 | semidirect |
| 36. #14556585 | C8 | semidirect |
| 65. #11924007 | C2×C8 | semidirect |
| 76. C42×C73 | C2×C8 | semidirect |
| 101. #10596833 | #126 | semidirect |
| 127. C73 | C8×#126 | semidirect |
| 196. C42 | #11924036 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22626002 | 2 |
| #22625986 | 2 |
| #22625858 | 2 |
| #22625723 | 2 |
| #22625665 | 2 |
| C42×#10596833 | 2 |
| #22612479 | 2 |
| C8×#126 | 73 |