Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
366 conjugacy classes of subgroups; only the 211 normal subgroups are shown.
This group has 366 conjugacy classes of subgroups — too many to draw. Only its 211 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. #22558126 | C2 | semidirect |
| 4. #22558125 | C2 | semidirect |
| 5. C67×#1311 | C2 | semidirect |
| 19. C16×D67 | C8 | semidirect |
| 35. C67⋊C16 | C2×C8 | semidirect |
| 39. C16×C67 | C2×C8 | semidirect |
| 61. D67 | #1311 | direct (N × H) |
| 66. #1311 | D67 | direct (N × H) |
| 67. C67 | C2×#1311 | semidirect |
| 101. C16 | C8×D67 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×C16×D67 | 2 |
| C82×D67 | 2 |
| #22558126 | 2 |
| #22558125 | 2 |
| C67×#1311 | 2 |
| C2×#1311 | 67 |