Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
396 conjugacy classes of subgroups; only the 217 normal subgroups are shown.
This group has 396 conjugacy classes of subgroups — too many to draw. Only its 217 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 |
|---|---|---|
| 2. Q8×#11764040 | C2 | semidirect |
| 3. C8×Dic274 | C2 | semidirect |
| 4. #22577527 | C2 | semidirect |
| 7. C8×Q8×C137 | C2 | semidirect |
| 25. Q8×D137 | C8 | semidirect |
| 73. C137 | #2982 | semidirect |
| 79. C8×Q8 | D137 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×Q8×D137 | 2 |
| Q8×#11764040 | 2 |
| C8×Dic274 | 2 |
| #22577527 | 2 |
| #22577455 | 2 |
| #22577454 | 2 |
| C8×Q8×C137 | 2 |
| #2982 | 137 |