Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
562 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 562 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. #22573184 | C2 | semidirect |
| 2. Q8×D536 | C2 | semidirect |
| 3. #22562433 | C2 | semidirect |
| 4. #22562347 | C2 | semidirect |
| 5. #22562245 | C2 | semidirect |
| 6. C4×D1072 | C2 | semidirect |
| 7. Q8×C16×C67 | C2 | semidirect |
| 59. D536 | #41 | semidirect |
| 74. Q8×C67 | D16 | semidirect |
| 116. Q8×C16 | D67 | semidirect |
| 118. C67 | #33925 | semidirect |
| 186. Q8 | D1072 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22573184 | 2 |
| Q8×D536 | 2 |
| #22562433 | 2 |
| #22562347 | 2 |
| #22562245 | 2 |
| C4×D1072 | 2 |
| Q8×C16×C67 | 2 |
| #33925 | 67 |