Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
394 conjugacy classes of subgroups; only the 158 normal subgroups are shown.
This group has 394 conjugacy classes of subgroups — too many to draw. Only its 158 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. #22578452 | C2 | semidirect |
| 2. #22578437 | C2 | semidirect |
| 3. #22578436 | C2 | semidirect |
| 4. #22578421 | C2 | semidirect |
| 5. #22578420 | C2 | semidirect |
| 6. #22578408 | C2 | semidirect |
| 7. #22578406 | C2 | semidirect |
| 64. Dic274 | M16 | semidirect |
| 107. C137 | #2991 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22578452 | 2 |
| #22578437 | 2 |
| #22578436 | 2 |
| #22578421 | 2 |
| #22578420 | 2 |
| #22578408 | 2 |
| #22578406 | 2 |
| #22577871 | 2 |
| #2991 | 137 |