Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
398 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 398 conjugacy classes of subgroups — too many to draw. Only its 101 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. #22626980 | C2 | direct (N × H) |
| 44. C2×Dic292 | C8 | semidirect |
| 48. Q16×D73 | C8 | semidirect |
| 51. C2×Q16×C73 | C8 | semidirect |
| 81. Dic292 | C2×C8 | semidirect |
| 91. Q16×C73 | C2×C8 | semidirect |
| 142. C2×C73 | #1334 | semidirect |
| 144. D73 | #1334 | semidirect |
| 151. C73 | C2×#1334 | semidirect |
| 174. C2×Q16 | #10596842 | semidirect |
| 216. Q16 | C2×#10596842 | semidirect |
| 291. C2 | #22626980 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17989682 | 2 |
| C2×#17989676 | 2 |
| #22626980 | 2 |
| C2×Q16×#64408 | 2 |
| C2×#1334 | 73 |