Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
552 conjugacy classes of subgroups; only the 181 normal subgroups are shown.
This group has 552 conjugacy classes of subgroups — too many to draw. Only its 181 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 |
|---|---|---|
| 4. #22577781 | C2 | direct (N × H) |
| 49. C2×Dic137 | Q16 | semidirect |
| 71. Dic137 | C2×Q16 | semidirect |
| 72. C2×C137 | #494 | semidirect |
| 75. C137 | C2×#494 | semidirect |
| 148. C2 | #22577781 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×Dic548 | 2 |
| C22×#14555500 | 2 |
| C2×#17984086 | 2 |
| #22577781 | 2 |
| C2×C8×Dic137 | 2 |
| C22×Q16×C137 | 2 |
| C2×#494 | 137 |