Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
370 conjugacy classes of subgroups; only the 139 normal subgroups are shown.
This group has 370 conjugacy classes of subgroups — too many to draw. Only its 139 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. #22578132 | C2 | semidirect |
| 3. #22577754 | C2 | semidirect |
| 4. #22577689 | C2 | semidirect |
| 7. C8×Q8×C137 | C2 | semidirect |
| 53. Q8×C137 | SD16 | semidirect |
| 74. C137 | #3359 | semidirect |
| 81. C8×Q8 | D137 | semidirect |
| 122. Q8 | #14555499 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22578132 | 2 |
| Q8×D548 | 2 |
| #22577754 | 2 |
| #22577689 | 2 |
| #22577609 | 2 |
| C4×#14555499 | 2 |
| C8×Q8×C137 | 2 |
| #3359 | 137 |