Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
282 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 282 conjugacy classes of subgroups — too many to draw. Only its 115 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 |
|---|---|---|
| 14. #17988415 | C4 | semidirect |
| 15. #17988413 | C4 | semidirect |
| 78. C16×C73 | C4⋊C4 | semidirect |
| 130. C73 | #13174 | semidirect |
| 201. C16 | #11924007 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22611719 | 2 |
| C2×#17988410 | 2 |
| #22610684 | 2 |
| #22610669 | 2 |
| #22608040 | 2 |
| #22608037 | 2 |
| C2×#347×C73 | 2 |
| #13174 | 73 |