Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
354 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 354 conjugacy classes of subgroups — too many to draw. Only its 101 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. C2×#17988410 | C2 | semidirect |
| 5. #22609837 | C2 | semidirect |
| 6. #22608030 | C2 | semidirect |
| 7. C73×#1377 | C2 | semidirect |
| 17. #17988401 | C4 | semidirect |
| 143. #1377 | D73 | semidirect |
| 144. C73 | #13138 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17988410 | 2 |
| C2×#17988401 | 2 |
| #22610807 | 2 |
| #22609837 | 2 |
| #22608030 | 2 |
| C73×#1377 | 2 |
| #13138 | 73 |