Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
496 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 496 conjugacy classes of subgroups — too many to draw. Only its 107 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 |
|---|---|---|
| 4. #22611650 | C2 | semidirect |
| 5. #22610844 | C2 | semidirect |
| 6. #22608019 | C2 | semidirect |
| 7. C73×#1382 | C2 | semidirect |
| 13. C2×#14556536 | C4 | semidirect |
| 33. C2×Dic292 | C2×C4 | semidirect |
| 59. C2×C16×C73 | C2×C4 | semidirect |
| 166. #1382 | D73 | semidirect |
| 168. C73 | #13019 | semidirect |
| 215. C2×C16 | C4×D73 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14556536 | 2 |
| #22618782 | 2 |
| C2×#17988399 | 2 |
| #22611650 | 2 |
| #22610844 | 2 |
| #22608019 | 2 |
| C73×#1382 | 2 |
| #13019 | 73 |