Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
558 conjugacy classes of subgroups; only the 151 normal subgroups are shown.
This group has 558 conjugacy classes of subgroups — too many to draw. Only its 151 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. #22570796 | C2 | semidirect |
| 3. #22562489 | C2 | semidirect |
| 4. #22562464 | C2 | semidirect |
| 5. #22562437 | C2 | semidirect |
| 6. #22562304 | C2 | semidirect |
| 7. #22562064 | C2 | semidirect |
| 8. C4×C16×D67 | C2 | semidirect |
| 9. C67×#2240 | C2 | semidirect |
| 101. C67⋊C16 | #41 | semidirect |
| 135. C4×D67 | SD32 | semidirect |
| 171. #2240 | D67 | semidirect |
| 175. C67 | #33736 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22570796 | 2 |
| #22570786 | 2 |
| #22562489 | 2 |
| #22562464 | 2 |
| #22562437 | 2 |
| #22562304 | 2 |
| #22562064 | 2 |
| C4×C16×D67 | 2 |
| C67×#2240 | 2 |
| #33736 | 67 |