Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
610 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 610 conjugacy classes of subgroups — too many to draw. Only its 113 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. C2×Q8⋊#10596842 | C2 | semidirect |
| 4. #22626939 | C2 | semidirect |
| 58. #14556571 | C8 | semidirect |
| 59. #14556570 | C8 | semidirect |
| 62. #14556567 | C8 | semidirect |
| 66. C22⋊Q8×C73 | C8 | semidirect |
| 235. C73 | #9073 | semidirect |
| 266. C22⋊Q8 | #10596842 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17989700 | 2 |
| #22627071 | 2 |
| C2×Q8⋊#10596842 | 2 |
| #22626939 | 2 |
| C22⋊Q8×#64408 | 2 |
| #9073 | 73 |