Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
440 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 440 conjugacy classes of subgroups — too many to draw. Only its 99 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. #22610909 | C2 | semidirect |
| 3. #22610082 | C2 | semidirect |
| 4. #22608621 | C2 | semidirect |
| 6. #22607806 | C2 | semidirect |
| 85. C4×Dic73 | SD16 | semidirect |
| 198. C73 | #10520 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22610909 | 2 |
| #22610760 | 2 |
| #22610082 | 2 |
| #22608621 | 2 |
| #22608608 | 2 |
| #22607806 | 2 |
| C73×#3246 | 2 |
| #10520 | 73 |