Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
538 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 538 conjugacy classes of subgroups — too many to draw. Only its 105 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. C4×C4⋊#10596842 | C2 | semidirect |
| 2. #22627065 | 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 |
| 216. C73 | #7560 | semidirect |
| 243. C4×D4 | #10596842 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×C4⋊#10596842 | 2 |
| #22627065 | 2 |
| #22626931 | 2 |
| #22626930 | 2 |
| #22626388 | 2 |
| #7560 | 73 |