Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
310 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 310 conjugacy classes of subgroups — too many to draw. Only its 93 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. #22578170 | C2 | semidirect |
| 2. #22577420 | C2 | semidirect |
| 3. #22577399 | C2 | semidirect |
| 4. #22577370 | C2 | semidirect |
| 5. #22577175 | C2 | semidirect |
| 6. #22577167 | C2 | semidirect |
| 22. #137×C137 | C4 | semidirect |
| 24. AGL(1,ℤ/8)×C137 | C4 | semidirect |
| 118. C137 | #1881 | semidirect |
| 130. #137 | Dic137 | semidirect |
| 132. AGL(1,ℤ/8) | Dic137 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22578170 | 2 |
| #22577420 | 2 |
| #22577399 | 2 |
| #22577370 | 2 |
| #22577175 | 2 |
| #22577167 | 2 |
| #575×C137 | 2 |
| #1881 | 137 |