Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
292 conjugacy classes of subgroups; only the 106 normal subgroups are shown.
This group has 292 conjugacy classes of subgroups — too many to draw. Only its 106 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C67 | #95 |
| commutator | C2×C4 | C4×C8×C67 |
| Frattini, cosocle | C23×C8 | C22×C67 |
| socle | C22×C67 | #336 |
| prime radical | C24×C67 | M16 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C67 ◁ C23×C8×C67 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 6. C22×C16×C67 | C4 | semidirect |
| 13. C22⋊C16×C67 | C4 | semidirect |
| 106. #7200 | C67 | direct (N × H) |
| 116. C67 | #7200 | direct (N × H) |
| 119. C22×C16 | C4×C67 | semidirect |
| 126. C22⋊C16 | C4×C67 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C67×#2112 | 2 |
| C2×C22⋊C16×C67 | 2 |
| C67×#1752 | 2 |
| #7200 | 67 |