Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
248 conjugacy classes of subgroups; only the 94 normal subgroups are shown.
This group has 248 conjugacy classes of subgroups — too many to draw. Only its 94 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C8×C67 | #99 |
| commutator | C23 | C4×C8×C67 |
| Frattini, cosocle | C2×#131 | C22×C67 |
| socle | C2×C67 | #1282 |
| prime radical | C2×#41×C67 | C2×C4 |
| LCS | G ▷ C23 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C8×C67 ◁ C2×C8×C67 ◁ C2×#131×C67 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 6. C2×M32×C67 | C4 | semidirect |
| 7. C22×C16×C67 | C4 | semidirect |
| 12. #349×C67 | C4 | semidirect |
| 108. #7207 | C67 | direct (N × H) |
| 117. C67 | #7207 | direct (N × H) |
| 120. C2×M32 | C4×C67 | semidirect |
| 121. C22×C16 | C4×C67 | semidirect |
| 126. #349 | C4×C67 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C67×#2115 | 2 |
| C67×#2113 | 2 |
| C67×#1757 | 2 |
| #7207 | 67 |