Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
2502 conjugacy classes of subgroups; only the 272 normal subgroups are shown.
This group has 2502 conjugacy classes of subgroups — too many to draw. Only its 272 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×#17989532 | C2 | semidirect |
| 2. #22625113 | C2 | semidirect |
| 8. C2×#14556588 | C4 | semidirect |
| 9. C2×#14556587 | C4 | semidirect |
| 12. C2×#127×C73 | C4 | semidirect |
| 44. C4×Dic73 | C22⋊C4 | semidirect |
| 49. C42×C73 | C22⋊C4 | semidirect |
| 91. C73 | #14661 | semidirect |
| 96. C2×#127 | #64408 | semidirect |
| 137. C42 | C22⋊#64408 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17989532 | 2 |
| #22625113 | 2 |
| C2×#127×D73 | 2 |
| #14661 | 73 |