Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
294 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 294 conjugacy classes of subgroups — too many to draw. Only its 63 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. #22612243 | C2 | semidirect |
| 2. #22612034 | C2 | semidirect |
| 3. #22608118 | C2 | semidirect |
| 4. #22608071 | C2 | semidirect |
| 5. C73×#3414 | C2 | semidirect |
| 6. C2×D1168 | C22 | semidirect |
| 10. #17988421 | C22 | semidirect |
| 11. #17988415 | C22 | semidirect |
| 35. Q32×C73 | D4 | semidirect |
| 39. D16×C73 | D4 | semidirect |
| 112. #3414 | D73 | semidirect |
| 117. C73 | #13667 | semidirect |
| 143. Q32 | C22⋊D73 | semidirect |
| 148. D16 | C22⋊D73 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22612243 | 2 |
| #22612034 | 2 |
| #22608118 | 2 |
| #22608071 | 2 |
| C73×#3414 | 2 |
| #13667 | 73 |