Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
692 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 692 conjugacy classes of subgroups — too many to draw. Only its 85 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. #22620918 | C2 | semidirect |
| 2. #22620022 | C2 | semidirect |
| 3. #22610849 | C2 | semidirect |
| 4. #22608529 | C2 | semidirect |
| 5. #22608374 | C2 | semidirect |
| 6. #22607787 | C2 | semidirect |
| 7. C73×#2540 | C2 | semidirect |
| 38. #14556591 | D4 | semidirect |
| 39. #14556588 | D4 | semidirect |
| 47. C4⋊#10596831 | D4 | semidirect |
| 57. #14556502 | D4 | semidirect |
| 241. #2540 | D73 | semidirect |
| 246. C73 | #10004 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22620918 | 2 |
| #22620022 | 2 |
| #22610849 | 2 |
| #22608529 | 2 |
| #22608374 | 2 |
| #22607787 | 2 |
| C73×#2540 | 2 |
| #10004 | 73 |