Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
484 conjugacy classes of subgroups; only the 189 normal subgroups are shown.
This group has 484 conjugacy classes of subgroups — too many to draw. Only its 189 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. #22577883 | C2 | semidirect |
| 3. #22577516 | C2 | semidirect |
| 4. #22577511 | C2 | semidirect |
| 5. C4×#14555499 | C2 | semidirect |
| 6. C2×#17984020 | C2 | semidirect |
| 7. #22577405 | C2 | semidirect |
| 8. #405×C137 | C2 | semidirect |
| 10. #17984110 | C4 | semidirect |
| 30. #14555510 | C2×C4 | semidirect |
| 37. Dic548 | C2×C4 | semidirect |
| 38. #14555499 | C2×C4 | semidirect |
| 39. D1096 | C2×C4 | semidirect |
| 47. C2×C8×C137 | C2×C4 | semidirect |
| 90. C137 | #2952 | semidirect |
| 99. #405 | D137 | semidirect |
| 133. C2×C8 | C4×D137 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17984110 | 2 |
| #22577883 | 2 |
| #22577516 | 2 |
| #22577511 | 2 |
| C4×#14555499 | 2 |
| C2×#17984020 | 2 |
| #22577405 | 2 |
| #405×C137 | 2 |
| #2952 | 137 |