Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
1006 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 1006 conjugacy classes of subgroups — too many to draw. Only its 123 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. #22627052 | C2 | semidirect |
| 2. #22627051 | C2 | semidirect |
| 3. #22627043 | C2 | semidirect |
| 4. #22627043 | C2 | semidirect |
| 67. C2×#11924029 | C8 | semidirect |
| 69. C2×#11924028 | C8 | semidirect |
| 71. C2×#11924027 | C8 | semidirect |
| 81. C2×#41×C73 | C8 | semidirect |
| 286. C73 | #8324 | semidirect |
| 317. C2×#41 | #10596842 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22627052 | 2 |
| #22627051 | 2 |
| #22627043 | 2 |
| C2×#17989656 | 2 |
| #8324 | 73 |