Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
4614 conjugacy classes of subgroups; only the 432 normal subgroups are shown.
This group has 4614 conjugacy classes of subgroups — too many to draw. Only its 432 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. C2×C4×C22⋊#64408 | C2 | semidirect |
| 2. #22625121 | C2 | semidirect |
| 3. #22625113 | C2 | semidirect |
| 9. C22×#11924029 | C4 | semidirect |
| 10. C22×#11924028 | C4 | semidirect |
| 11. C22×#11924027 | C4 | semidirect |
| 16. C22×#41×C73 | C4 | semidirect |
| 48. C22×#64408 | #41 | semidirect |
| 69. C22×Dic73 | C22⋊C4 | semidirect |
| 76. C2×C4×D73 | C22⋊C4 | semidirect |
| 77. C2×C4×D73 | C22⋊C4 | semidirect |
| 86. C22×C4×C73 | C22⋊C4 | semidirect |
| 150. C73 | #13851 | semidirect |
| 155. C22×#41 | #64408 | semidirect |
| 230. C22×C4 | C22⋊#64408 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×C22⋊#64408 | 2 |
| #22625121 | 2 |
| #22625113 | 2 |
| C22×#41×D73 | 2 |
| #13851 | 73 |