Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
182 conjugacy classes of subgroups; only the 70 normal subgroups are shown.
This group has 182 conjugacy classes of subgroups — too many to draw. Only its 70 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 | #327 |
| commutator | C2×C8 | C2×C8×C67 |
| Frattini, cosocle | C2×#97 | C22×C67 |
| socle | C2×C67 | #1271 |
| prime radical | C23×C67 | #104 |
| LCS | G ▷ C2×C8 ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C67 ◁ C22×C4×C67 ◁ C2×#97×C67 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 21. #106×C67 | C8 | semidirect |
| 77. #7125 | C67 | direct (N × H) |
| 85. C67 | #7125 | direct (N × H) |
| 103. #106 | C8×C67 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C67×#1946 | 2 |
| C67×#1375 | 2 |
| C67×#1281 | 2 |
| #7125 | 67 |