Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
424 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 424 conjugacy classes of subgroups — too many to draw. Only its 141 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. #22577765 | C2 | semidirect |
| 3. #22577755 | C2 | semidirect |
| 4. #22577751 | C2 | semidirect |
| 5. #22577402 | C2 | semidirect |
| 6. C4×#14555494 | C2 | semidirect |
| 7. C2×C4⋊Q8×C137 | C2 | semidirect |
| 100. C137 | #3141 | semidirect |
| 103. C2×C4⋊Q8 | D137 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22577953 | 2 |
| #22577765 | 2 |
| #22577755 | 2 |
| #22577751 | 2 |
| #22577402 | 2 |
| C4×#14555494 | 2 |
| C2×C4⋊Q8×C137 | 2 |
| #3141 | 137 |