Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
1538 conjugacy classes of subgroups; only the 366 normal subgroups are shown.
This group has 1538 conjugacy classes of subgroups — too many to draw. Only its 366 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C67 | C22×C22⋊C4 |
| commutator | C23 | C23×C4×C67 |
| Frattini, cosocle | C24 | C24×C67 |
| prime radical | C2×#534×C67 | C2 |
| LCS | G ▷ C23 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C67 ◁ C22×C22⋊C4×C67 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C67×#2312 | C2 | semidirect |
| 3. C67×#1964 | C2 | semidirect |
| 4. C67×#1781 | C2 | semidirect |
| 7. C2×#123×C67 | C4 | semidirect |
| 9. C2×#120×C67 | C4 | semidirect |
| 11. C2×#99×C67 | C22 | semidirect |
| 13. #380×C67 | C22 | semidirect |
| 15. C4×C22⋊C4×C67 | C22 | semidirect |
| 121. #21795 | C67 | direct (N × H) |
| 129. #2312 | C2×C67 | semidirect |
| 130. #1964 | C2×C67 | semidirect |
| 131. #1781 | C2×C67 | semidirect |
| 132. C67 | #21795 | direct (N × H) |
| 135. C2×#123 | C4×C67 | semidirect |
| 137. C2×#120 | C4×C67 | semidirect |
| 139. C2×#99 | C22×C67 | semidirect |
| 141. #380 | C22×C67 | semidirect |
| 143. C4×C22⋊C4 | C22×C67 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#534×C67 | 2 |
| C67×#2312 | 2 |
| C67×#1964 | 2 |
| C67×#1781 | 2 |
| #21795 | 67 |