Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
794 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 794 conjugacy classes of subgroups — too many to draw. Only its 103 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. #22571129 | C2 | semidirect |
| 2. #22569673 | C2 | semidirect |
| 3. #22565155 | C2 | semidirect |
| 4. #22558876 | C2 | semidirect |
| 5. #22558705 | C2 | semidirect |
| 6. #22558111 | C2 | semidirect |
| 7. C67×#1478 | C2 | semidirect |
| 42. #14524043 | D4 | semidirect |
| 47. #14524040 | D4 | semidirect |
| 60. C4⋊(C67⋊C8) | D4 | semidirect |
| 75. C4⋊C8×C67 | D4 | semidirect |
| 127. C2×D4×C67 | D8 | semidirect |
| 246. #1478 | D67 | semidirect |
| 248. C67 | #10238 | semidirect |
| 312. C4⋊C8 | C22⋊D67 | semidirect |
| 352. C2×D4 | D536 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22571129 | 2 |
| #22569673 | 2 |
| #22565155 | 2 |
| #22558876 | 2 |
| #22558705 | 2 |
| #22558111 | 2 |
| C67×#1478 | 2 |
| #10238 | 67 |