Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
198 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 198 conjugacy classes of subgroups — too many to draw. Only its 75 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 |
|---|---|---|
| 62. C16×C73 | Q16 | semidirect |
| 102. C73 | #12459 | semidirect |
| 157. C16 | #11924018 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22612213 | 2 |
| #22609335 | 2 |
| #22609325 | 2 |
| #22608005 | 2 |
| #22607988 | 2 |
| #22607985 | 2 |
| Q8×C16×C73 | 2 |
| #12459 | 73 |