Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
362 conjugacy classes of subgroups; only the 59 normal subgroups are shown.
This group has 362 conjugacy classes of subgroups — too many to draw. Only its 59 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. #22618200 | C2 | semidirect |
| 4. #22607960 | C2 | semidirect |
| 5. #22607957 | C2 | semidirect |
| 6. #22607877 | C2 | semidirect |
| 104. C42×C73 | SD16 | semidirect |
| 181. C73 | #12183 | semidirect |
| 278. C42 | #11924016 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22618200 | 2 |
| #22608968 | 2 |
| #22608900 | 2 |
| #22607960 | 2 |
| #22607957 | 2 |
| #22607877 | 2 |
| C73×#2039 | 2 |
| #12183 | 73 |