Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
456 conjugacy classes of subgroups; only the 102 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 102 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 | #392 |
| commutator, Frattini, cosocle | C2×C42 | C23×C67 |
| prime radical | #532×C67 | C22 |
| LCS | G ▷ C2×C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C67 ◁ C2×C42×C67 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. C2×#491×C67 | C2 | semidirect |
| 4. C67×#1556 | C2 | semidirect |
| 6. C67×#1470 | C2 | semidirect |
| 7. C67×#1302 | C2 | semidirect |
| 163. #10134 | C67 | direct (N × H) |
| 171. C2×#491 | C2×C67 | semidirect |
| 172. #1556 | C2×C67 | semidirect |
| 174. #1470 | C2×C67 | semidirect |
| 175. #1302 | C2×C67 | semidirect |
| 176. C67 | #10134 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C67×#3234 | 2 |
| C67×#3227 | 2 |
| C2×#491×C67 | 2 |
| C67×#1556 | 2 |
| C67×#1530 | 2 |
| C67×#1470 | 2 |
| C67×#1302 | 2 |
| #10134 | 67 |