Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
632 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 632 conjugacy classes of subgroups — too many to draw. Only its 99 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. #22570218 | C2 | semidirect |
| 2. #22570006 | C2 | semidirect |
| 4. #22558774 | C2 | semidirect |
| 5. #22558635 | C2 | semidirect |
| 6. #22558068 | C2 | semidirect |
| 7. C67×#1478 | C2 | semidirect |
| 38. #14524043 | D4 | semidirect |
| 39. #14524043 | D4 | semidirect |
| 61. C4⋊(C67⋊C8) | D4 | semidirect |
| 83. C4×C8×C67 | D4 | semidirect |
| 127. C2×D4×C67 | SD16 | semidirect |
| 243. #1478 | D67 | semidirect |
| 245. C67 | #10000 | semidirect |
| 318. C4×C8 | C22⋊D67 | semidirect |
| 337. C2×D4 | #11761617 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22570218 | 2 |
| #22570006 | 2 |
| #22565106 | 2 |
| #22558774 | 2 |
| #22558635 | 2 |
| #22558068 | 2 |
| C67×#1478 | 2 |
| #10000 | 67 |