Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
284 conjugacy classes of subgroups; only the 66 normal subgroups are shown.
This group has 284 conjugacy classes of subgroups — too many to draw. Only its 66 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. #22578413 | C2 | semidirect |
| 2. #22578402 | C2 | semidirect |
| 3. #22578401 | C2 | semidirect |
| 4. #22578384 | C2 | semidirect |
| 5. #22578383 | C2 | semidirect |
| 6. #22578366 | C2 | semidirect |
| 26. C2×#14555500 | C4 | semidirect |
| 27. C2×#14555499 | C4 | semidirect |
| 28. C2×#14555495 | C4 | semidirect |
| 30. C2×SD16×C137 | C4 | semidirect |
| 132. C137 | #1976 | semidirect |
| 149. C2×SD16 | #10587739 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22578413 | 2 |
| #22578402 | 2 |
| #22578401 | 2 |
| #22578384 | 2 |
| #22578383 | 2 |
| #22578366 | 2 |
| C2×#17984109 | 2 |
| #1976 | 137 |