Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
934 conjugacy classes of subgroups; only the 128 normal subgroups are shown.
This group has 934 conjugacy classes of subgroups — too many to draw. Only its 128 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×#17989500 | C2 | semidirect |
| 13. C22×Dic292 | C4 | semidirect |
| 18. C2×Q16×D73 | C4 | semidirect |
| 21. C22×Q16×C73 | C4 | semidirect |
| 93. Dic292 | C22⋊C4 | semidirect |
| 111. Q16×C73 | C22⋊C4 | semidirect |
| 158. C22×C73 | #358 | semidirect |
| 164. C2×D73 | #358 | semidirect |
| 189. C73 | #12732 | semidirect |
| 198. C22×Q16 | #64408 | semidirect |
| 285. Q16 | C22⋊#64408 | semidirect |
| 352. C22 | #17989500 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17989500 | 2 |
| #22626156 | 2 |
| #22625808 | 2 |
| C22×Q16×D73 | 2 |
| #12732 | 73 |