Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
272 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 272 conjugacy classes of subgroups — too many to draw. Only its 71 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 |
|---|---|---|
| 71. Q16×C73 | Q16 | semidirect |
| 137. C73 | #12415 | semidirect |
| 196. Q16 | #11924018 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22612218 | 2 |
| #22612083 | 2 |
| #22609449 | 2 |
| #22607983 | 2 |
| #22607913 | 2 |
| #22607901 | 2 |
| C73×#3390 | 2 |
| #12415 | 73 |