Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
402 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 402 conjugacy classes of subgroups — too many to draw. Only its 105 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. #22561802 | C2 | semidirect |
| 3. #334×D67 | C2 | semidirect |
| 4. #22558179 | C2 | semidirect |
| 5. #22558177 | C2 | semidirect |
| 6. #22558175 | C2 | semidirect |
| 7. C67×#1334 | C2 | semidirect |
| 29. #14524066 | C8 | semidirect |
| 75. D536 | C2×C8 | semidirect |
| 96. Q16×C67 | C2×C8 | semidirect |
| 162. #1334 | D67 | semidirect |
| 165. C67 | #11598 | semidirect |
| 233. Q16 | C8×D67 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#14524066 | 2 |
| #22561802 | 2 |
| #334×D67 | 2 |
| #22558179 | 2 |
| #22558177 | 2 |
| #22558175 | 2 |
| C67×#1334 | 2 |
| #11598 | 67 |