Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
424 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 424 conjugacy classes of subgroups — too many to draw. Only its 86 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C67 | #2044 |
| commutator, Frattini, cosocle | C2×#41 | C23×C67 |
| prime radical | #535×C67 | C22 |
| LCS | G ▷ C2×#41 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C67 ◁ C2×C4×C67 ◁ C2×#41×C67 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C67×#2129 | C2 | semidirect |
| 4. C67×#1915 | C2 | semidirect |
| 6. C67×#1868 | C2 | semidirect |
| 7. C67×#1395 | C2 | semidirect |
| 188. #13433 | C67 | direct (N × H) |
| 196. #2129 | C2×C67 | semidirect |
| 198. #1915 | C2×C67 | semidirect |
| 200. #1868 | C2×C67 | semidirect |
| 201. #1395 | C2×C67 | semidirect |
| 202. C67 | #13433 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C67×#3200 | 2 |
| C67×#2129 | 2 |
| C67×#2122 | 2 |
| C67×#1915 | 2 |
| C67×#1910 | 2 |
| C67×#1868 | 2 |
| C67×#1395 | 2 |
| #13433 | 67 |