Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
356 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 356 conjugacy classes of subgroups — too many to draw. Only its 145 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. #22577806 | C2 | semidirect |
| 3. #22577803 | C2 | semidirect |
| 4. #22577801 | C2 | semidirect |
| 7. #498×C137 | C2 | semidirect |
| 28. C8×D137 | Q8 | semidirect |
| 67. C137 | #3160 | semidirect |
| 73. #498 | D137 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22577958 | 2 |
| #22577806 | 2 |
| #22577803 | 2 |
| #22577801 | 2 |
| #22577438 | 2 |
| C4×C8×D137 | 2 |
| #498×C137 | 2 |
| #3160 | 137 |