Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
668 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 668 conjugacy classes of subgroups — too many to draw. Only its 165 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. C22×#14555497 | C2 | semidirect |
| 2. C22×#14555495 | C2 | semidirect |
| 3. C2×#17984085 | C2 | semidirect |
| 4. #22577793 | C2 | direct (N × H) |
| 5. C2×#17983999 | C2 | semidirect |
| 6. C2×#124×C137 | C2 | semidirect |
| 10. C2×#14555497 | C22 | semidirect |
| 12. C2×#14555495 | C22 | semidirect |
| 15. #17984085 | C22 | semidirect |
| 16. #17983999 | C22 | semidirect |
| 20. #124×C137 | C22 | semidirect |
| 32. C2×#11764040 | D4 | semidirect |
| 54. #11764040 | C2×D4 | semidirect |
| 84. C2×C137 | #496 | semidirect |
| 88. C137 | C2×#496 | semidirect |
| 93. C2×#124 | D137 | semidirect |
| 108. #124 | C2×D137 | semidirect |
| 174. C2 | #22577793 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14555497 | 2 |
| C22×#14555495 | 2 |
| C2×#17984085 | 2 |
| #22577793 | 2 |
| C2×#17983999 | 2 |
| C2×#124×C137 | 2 |
| C2×#496 | 137 |