Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
626 conjugacy classes of subgroups; only the 175 normal subgroups are shown.
This group has 626 conjugacy classes of subgroups — too many to draw. Only its 175 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. #22558054 | C2 | semidirect |
| 4. #22558053 | C2 | semidirect |
| 5. C67×#1281 | C2 | semidirect |
| 65. C2×C67⋊C8 | M16 | semidirect |
| 79. C2×C8×C67 | M16 | semidirect |
| 137. #1281 | D67 | semidirect |
| 138. C67 | #7919 | semidirect |
| 205. C2×C8 | #11761611 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22568837 | 2 |
| C2×#97×D67 | 2 |
| #22558054 | 2 |
| #22558053 | 2 |
| C67×#1281 | 2 |
| #7919 | 67 |