Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
2594 conjugacy classes of subgroups; only the 302 normal subgroups are shown.
This group has 2594 conjugacy classes of subgroups — too many to draw. Only its 302 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C67 | #120 |
| commutator | C23 | C2×C42×C67 |
| Frattini, cosocle | C25 | C23×C67 |
| prime radical | C26×C67 | C22 |
| LCS | G ▷ C23 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C67 ◁ C25×C67 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C67×#2273 | C2 | semidirect |
| 3. C2×#342×C67 | C2 | semidirect |
| 9. #379×C67 | C4 | semidirect |
| 48. C24×C67 | C42 | semidirect |
| 59. C22×C4×C67 | C22⋊C4 | semidirect |
| 129. #10935 | C67 | direct (N × H) |
| 137. #2273 | C2×C67 | semidirect |
| 138. C2×#342 | C2×C67 | semidirect |
| 139. C67 | #10935 | direct (N × H) |
| 145. #379 | C4×C67 | semidirect |
| 184. C24 | C42×C67 | semidirect |
| 195. C22×C4 | C22⋊C4×C67 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#379×C67 | 2 |
| C67×#2273 | 2 |
| C2×#342×C67 | 2 |
| #10935 | 67 |