Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
472 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 472 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 |
|---|---|---|
| 3. C2×#17988402 | C2 | semidirect |
| 5. #22610800 | C2 | semidirect |
| 6. #22608010 | C2 | semidirect |
| 7. C73×#1383 | C2 | semidirect |
| 13. C2×Dic584 | C4 | semidirect |
| 14. C2×#14556536 | C4 | semidirect |
| 175. #1383 | D73 | semidirect |
| 177. C73 | #13039 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17989030 | 2 |
| C2×#17988708 | 2 |
| C2×#17988402 | 2 |
| C2×#17988396 | 2 |
| #22610800 | 2 |
| #22608010 | 2 |
| C73×#1383 | 2 |
| #13039 | 73 |