Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
388 conjugacy classes of subgroups; only the 156 normal subgroups are shown.
This group has 388 conjugacy classes of subgroups — too many to draw. Only its 156 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. #22578454 | C2 | semidirect |
| 2. #22578437 | C2 | semidirect |
| 3. #22578433 | C2 | semidirect |
| 4. #22578426 | C2 | semidirect |
| 5. #22578421 | C2 | semidirect |
| 6. #22578408 | C2 | semidirect |
| 7. #22578404 | C2 | semidirect |
| 78. C4×D137 | M16 | semidirect |
| 107. C137 | #2989 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22578454 | 2 |
| #22578437 | 2 |
| #22578433 | 2 |
| #22578426 | 2 |
| #22578421 | 2 |
| #22578408 | 2 |
| #22578404 | 2 |
| C4×#14555511 | 2 |
| #2989 | 137 |