Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
1482 conjugacy classes of subgroups; only the 298 normal subgroups are shown.
This group has 1482 conjugacy classes of subgroups — too many to draw. Only its 298 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 | C2×#120 |
| commutator, Frattini, cosocle | C24 | C24×C67 |
| prime radical | C2×H(5,𝔽2)×C67 | C22 |
| LCS | G ▷ C24 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C67 ◁ C23×C4×C67 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. C67×#2486 | C2 | semidirect |
| 4. C67×#1890 | C2 | semidirect |
| 5. C67×#1799 | C2 | semidirect |
| 14. C22×C4⋊C4×C67 | C22 | semidirect |
| 20. #381×C67 | C22 | semidirect |
| 22. #380×C67 | C22 | semidirect |
| 23. #342×C67 | C22 | semidirect |
| 168. C4×C67 | #458 | semidirect |
| 169. #32927 | C67 | direct (N × H) |
| 178. #2486 | C2×C67 | semidirect |
| 179. #1890 | C2×C67 | semidirect |
| 180. #1799 | C2×C67 | semidirect |
| 181. C67 | #32927 | direct (N × H) |
| 190. C22×C4⋊C4 | C22×C67 | semidirect |
| 196. #381 | C22×C67 | semidirect |
| 198. #380 | C22×C67 | semidirect |
| 199. #342 | C22×C67 | semidirect |
| 344. C4 | #458×C67 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×H(5,𝔽2)×C67 | 2 |
| C2×#458×C67 | 2 |
| C67×#2486 | 2 |
| C67×#1890 | 2 |
| C67×#1799 | 2 |
| #32927 | 67 |