Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
214 conjugacy classes of subgroups; only the 92 normal subgroups are shown.
This group has 214 conjugacy classes of subgroups — too many to draw. Only its 92 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 |
|---|---|---|
| 2. #22578245 | C2 | semidirect |
| 3. #22578244 | C2 | semidirect |
| 4. C8×#11764047 | C2 | semidirect |
| 32. #11764047 | M16 | semidirect |
| 40. #11764040 | M16 | semidirect |
| 44. C8×C137 | M16 | semidirect |
| 56. C137 | #1455 | semidirect |
| 101. C8 | #14555520 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#14555520 | 2 |
| #22578245 | 2 |
| #22578244 | 2 |
| C8×#11764047 | 2 |
| #22577355 | 2 |
| #1455 | 137 |