Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
794 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 794 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. #22620849 | C2 | semidirect |
| 2. #22619395 | C2 | semidirect |
| 3. #22608599 | C2 | semidirect |
| 4. #22608425 | C2 | semidirect |
| 5. #22608322 | C2 | semidirect |
| 6. #22607834 | C2 | semidirect |
| 7. C73×#2541 | C2 | semidirect |
| 38. #14556591 | D4 | semidirect |
| 39. #14556588 | D4 | semidirect |
| 47. C4⋊#10596831 | D4 | semidirect |
| 48. C4⋊#10596831 | D4 | semidirect |
| 124. C2×D4×C73 | D8 | semidirect |
| 243. #2541 | D73 | semidirect |
| 248. C73 | #10238 | semidirect |
| 352. C2×D4 | #11924013 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22620849 | 2 |
| #22619395 | 2 |
| #22608599 | 2 |
| #22608425 | 2 |
| #22608322 | 2 |
| #22607834 | 2 |
| C73×#2541 | 2 |
| #10238 | 73 |