Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
402 conjugacy classes of subgroups; only the 221 normal subgroups are shown.
This group has 402 conjugacy classes of subgroups — too many to draw. Only its 221 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. Q8×#11764040 | C2 | semidirect |
| 2. #22577481 | C2 | semidirect |
| 3. #22577460 | C2 | semidirect |
| 4. C4×#14555494 | C2 | semidirect |
| 36. #11764040 | #41 | semidirect |
| 38. Q8×C137 | M16 | semidirect |
| 63. C137 | #2971 | semidirect |
| 100. Q8 | #14555494 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×#11764040 | 2 |
| #22577481 | 2 |
| #22577460 | 2 |
| C4×#14555494 | 2 |
| C4×#41×C137 | 2 |
| #2971 | 137 |