Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
380 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 380 conjugacy classes of subgroups — too many to draw. Only its 125 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 |
|---|---|---|
| 3. #22577770 | C2 | semidirect |
| 4. #22577755 | C2 | semidirect |
| 5. #22577754 | C2 | semidirect |
| 6. #22577753 | C2 | semidirect |
| 9. #487×C137 | C2 | semidirect |
| 106. C137 | #3139 | semidirect |
| 114. #487 | D137 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22577958 | 2 |
| C4⋊Q8×D137 | 2 |
| #22577770 | 2 |
| #22577755 | 2 |
| #22577754 | 2 |
| #22577753 | 2 |
| #22577410 | 2 |
| C4×#14555493 | 2 |
| #487×C137 | 2 |
| #3139 | 137 |