Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
898 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 898 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. #22627071 | C2 | semidirect |
| 3. #22626940 | C2 | semidirect |
| 47. C2×C22⋊Dic73 | C8 | semidirect |
| 48. C2×#11924005 | C8 | semidirect |
| 49. C2×#11924005 | C8 | semidirect |
| 52. C2×C22⋊C4×C73 | C8 | semidirect |
| 125. C23×C73 | C4⋊C8 | semidirect |
| 153. C22×D73 | C4⋊C8 | semidirect |
| 269. C73 | #8559 | semidirect |
| 306. C2×C22⋊C4 | #10596842 | semidirect |
| 423. C23 | C4⋊#10596842 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22627071 | 2 |
| C2×#17989672 | 2 |
| #22626940 | 2 |
| C2×C22⋊C4×#64408 | 2 |
| #8559 | 73 |