Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
360 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 87 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. #22612187 | C2 | semidirect |
| 2. #22612186 | C2 | semidirect |
| 3. #22612180 | C2 | semidirect |
| 4. #22609545 | C2 | semidirect |
| 5. #22609536 | C2 | semidirect |
| 6. #22607847 | C2 | semidirect |
| 7. C73×#2246 | C2 | semidirect |
| 53. #11924003 | D8 | semidirect |
| 65. C16×C73 | D8 | semidirect |
| 106. #2246 | D73 | semidirect |
| 110. C73 | #12519 | semidirect |
| 168. C16 | #11924013 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22612187 | 2 |
| #22612186 | 2 |
| #22612180 | 2 |
| #22609545 | 2 |
| #22609536 | 2 |
| #22607847 | 2 |
| C73×#2246 | 2 |
| #12519 | 73 |