Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
592 conjugacy classes of subgroups; only the 104 normal subgroups are shown.
This group has 592 conjugacy classes of subgroups — too many to draw. Only its 104 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 |
|---|---|---|
| 1. C2×#17984151 | C2 | semidirect |
| 13. C22×Dic274 | C4 | semidirect |
| 17. C2×Q8×D137 | C4 | semidirect |
| 21. C22×Q8×C137 | C4 | semidirect |
| 69. Dic274 | C22⋊C4 | semidirect |
| 84. Q8×C137 | C22⋊C4 | semidirect |
| 92. C22×C137 | #103 | semidirect |
| 98. C2×D137 | #103 | semidirect |
| 117. C137 | #1787 | semidirect |
| 130. C22×Q8 | #10587739 | semidirect |
| 187. Q8 | C22⋊#10587739 | semidirect |
| 219. C22 | #17984151 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17984151 | 2 |
| #22578371 | 2 |
| #22578345 | 2 |
| C22×Q8×D137 | 2 |
| #1787 | 137 |