Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
532 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 532 conjugacy classes of subgroups — too many to draw. Only its 97 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. #22573343 | C2 | semidirect |
| 2. #22569871 | C2 | semidirect |
| 3. C2×#16863206 | C2 | semidirect |
| 4. #22561936 | C2 | semidirect |
| 5. #22561837 | C2 | semidirect |
| 6. #22558309 | C2 | semidirect |
| 7. C67×#3067 | C2 | semidirect |
| 56. C2×C67⋊C16 | D4 | semidirect |
| 72. C2×Q16×C67 | D4 | semidirect |
| 74. C2×D8×C67 | D4 | semidirect |
| 85. #108×C67 | D4 | semidirect |
| 228. #3067 | D67 | semidirect |
| 234. C67 | #13318 | semidirect |
| 277. C2×Q16 | C22⋊D67 | semidirect |
| 281. C2×D8 | C22⋊D67 | semidirect |
| 308. #108 | C22⋊D67 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22573343 | 2 |
| #22569871 | 2 |
| C2×#16863206 | 2 |
| #22561936 | 2 |
| #22561837 | 2 |
| #22558309 | 2 |
| C67×#3067 | 2 |
| #13318 | 67 |