Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
286 conjugacy classes of subgroups; only the 66 normal subgroups are shown.
This group has 286 conjugacy classes of subgroups — too many to draw. Only its 66 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C4×C67 | #354 |
| commutator | C42 | C42×C67 |
| Frattini, cosocle | #532 | C22×C67 |
| socle | C2×C67 | #1393 |
| prime radical | #532×C67 | C22 |
| LCS | G ▷ C42 ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C67 ◁ C2×C4×C67 ◁ C22×C4×C67 ◁ #532×C67 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 9. #355×C67 | C4 | semidirect |
| 80. #7501 | C67 | direct (N × H) |
| 87. C67 | #7501 | direct (N × H) |
| 94. #355 | C4×C67 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C67×#2132 | 2 |
| C67×#1962 | 2 |
| #7501 | 67 |