Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
184 conjugacy classes of subgroups; only the 70 normal subgroups are shown.
This group has 184 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, socle | C2×C67 | #2215 |
| commutator, Frattini, cosocle | C2×C16 | C23×C67 |
| prime radical | C67×#2221 | C2 |
| LCS | G ▷ C2×C16 ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C67 ◁ C2×C4×C67 ◁ #131×C67 ◁ #504×C67 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×SD64×C67 | C2 | semidirect |
| 2. C67×#2258 | C2 | semidirect |
| 3. C67×#2222 | C2 | semidirect |
| 5. C67×#1425 | C2 | semidirect |
| 6. C67×#1420 | C2 | semidirect |
| 7. C67×#1419 | C2 | semidirect |
| 87. #13702 | C67 | direct (N × H) |
| 92. C2×SD64 | C2×C67 | semidirect |
| 93. #2258 | C2×C67 | semidirect |
| 94. #2222 | C2×C67 | semidirect |
| 96. #1425 | C2×C67 | semidirect |
| 97. #1420 | C2×C67 | semidirect |
| 98. #1419 | C2×C67 | semidirect |
| 99. C67 | #13702 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×SD64×C67 | 2 |
| C67×#2258 | 2 |
| C67×#2222 | 2 |
| C67×#2221 | 2 |
| C67×#1425 | 2 |
| C67×#1420 | 2 |
| C67×#1419 | 2 |
| #13702 | 67 |