Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
234 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 234 conjugacy classes of subgroups — too many to draw. Only its 71 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. #22612155 | C2 | semidirect |
| 2. #22609330 | C2 | semidirect |
| 4. #22608005 | C2 | semidirect |
| 5. #22607988 | C2 | semidirect |
| 6. #22607978 | C2 | semidirect |
| 7. D4×C16×C73 | C2 | semidirect |
| 113. D4×C16 | D73 | semidirect |
| 119. C73 | #12468 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22612155 | 2 |
| #22609330 | 2 |
| #22609286 | 2 |
| #22608005 | 2 |
| #22607988 | 2 |
| #22607978 | 2 |
| D4×C16×C73 | 2 |
| #12468 | 73 |