Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
520 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 520 conjugacy classes of subgroups — too many to draw. Only its 103 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. #22627073 | C2 | semidirect |
| 2. C4×C4⋊#10596842 | C2 | semidirect |
| 3. #22626931 | C2 | semidirect |
| 50. C4×D292 | C8 | semidirect |
| 51. D4×Dic73 | C8 | semidirect |
| 52. #14556553 | C8 | semidirect |
| 58. C4×D4×C73 | C8 | semidirect |
| 220. C73 | #7574 | semidirect |
| 247. C4×D4 | #10596842 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22627073 | 2 |
| C4×C4⋊#10596842 | 2 |
| #22626931 | 2 |
| #22626930 | 2 |
| #22626388 | 2 |
| #7574 | 73 |