Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
464 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 464 conjugacy classes of subgroups — too many to draw. Only its 89 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. #22615155 | C2 | semidirect |
| 5. #22607798 | C2 | semidirect |
| 6. #22607778 | C2 | semidirect |
| 7. C73×#1294 | C2 | semidirect |
| 227. #1294 | D73 | semidirect |
| 230. C73 | #10376 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22615155 | 2 |
| #22610766 | 2 |
| #22608500 | 2 |
| C2×#17988320 | 2 |
| #22607798 | 2 |
| #22607778 | 2 |
| C73×#1294 | 2 |
| #10376 | 73 |