Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
420 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 420 conjugacy classes of subgroups — too many to draw. Only its 141 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. #22577753 | C2 | semidirect |
| 3. #22577731 | C2 | semidirect |
| 4. #22577688 | C2 | semidirect |
| 5. #22577634 | C2 | semidirect |
| 6. #22577605 | C2 | semidirect |
| 7. #22577542 | C2 | semidirect |
| 8. C4×#14555497 | C2 | semidirect |
| 9. D4×#11764040 | C2 | semidirect |
| 10. C2×#17984012 | C2 | semidirect |
| 11. D4×Q8×C137 | C2 | semidirect |
| 94. Q8×C137 | #41 | semidirect |
| 95. D4×C137 | SD16 | semidirect |
| 128. C137 | #3298 | semidirect |
| 130. D4×Q8 | D137 | semidirect |
| 213. Q8 | #14555509 | semidirect |
| 217. D4 | #14555497 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22578057 | 2 |
| #22577753 | 2 |
| #22577731 | 2 |
| #22577688 | 2 |
| #22577634 | 2 |
| #22577605 | 2 |
| #22577542 | 2 |
| C4×#14555497 | 2 |
| D4×#11764040 | 2 |
| C2×#17984012 | 2 |
| D4×Q8×C137 | 2 |
| #3298 | 137 |