Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
456 conjugacy classes of subgroups; only the 175 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 175 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 |
|---|---|---|
| 3. #22577511 | C2 | semidirect |
| 4. #22577510 | C2 | semidirect |
| 5. #22577509 | C2 | semidirect |
| 6. C4×#14555500 | C2 | semidirect |
| 7. #22577495 | C2 | semidirect |
| 11. #441×C137 | C2 | semidirect |
| 15. Q16×D137 | C4 | semidirect |
| 108. C137 | #2950 | semidirect |
| 115. #441 | D137 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×Q16×D137 | 2 |
| #22577879 | 2 |
| #22577511 | 2 |
| #22577510 | 2 |
| #22577509 | 2 |
| C4×#14555500 | 2 |
| #22577495 | 2 |
| #22577438 | 2 |
| #22577410 | 2 |
| #22577360 | 2 |
| #441×C137 | 2 |
| #2950 | 137 |