Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
398 conjugacy classes of subgroups; only the 108 normal subgroups are shown.
This group has 398 conjugacy classes of subgroups — too many to draw. Only its 108 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 |
|---|---|---|
| 3. #22624892 | C2 | semidirect |
| 4. #22624891 | C2 | semidirect |
| 32. Q16×D73 | C8 | semidirect |
| 70. Dic292 | C2×C8 | semidirect |
| 90. Q16×C73 | C2×C8 | semidirect |
| 144. D73 | #1334 | semidirect |
| 150. C73 | C2×#1334 | semidirect |
| 216. Q16 | #11924036 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22626132 | 2 |
| #22625473 | 2 |
| #22624892 | 2 |
| #22624891 | 2 |
| C4×Q16×D73 | 2 |
| C2×#1334 | 73 |