Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
262 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 262 conjugacy classes of subgroups — too many to draw. Only its 115 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. #22558278 | C2 | semidirect |
| 4. #22558273 | C2 | semidirect |
| 5. C67×#1367 | C2 | semidirect |
| 48. C8×D67 | C16 | semidirect |
| 103. #1367 | D67 | semidirect |
| 104. C67 | #12012 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22562007 | 2 |
| C82×D67 | 2 |
| #22558278 | 2 |
| #22558273 | 2 |
| C67×#1367 | 2 |
| #12012 | 67 |