Finite Group DatabasebetaFinite Group Databasebeta← C2×C3×C17×C3⋊(C7⋊D7) #44473018
Order 29988.
440 conjugacy classes of subgroups; only the 172 normal subgroups are shown.
This group has 440 conjugacy classes of subgroups — too many to draw. Only its 172 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C3×C17 | C3⋊(C7⋊D7) |
| commutator, cosocle, hypocenter | C3×C72 | C22×C3×C17 |
| Frattini | C1 | G |
| Fitting, socle | C2×C32×C72×C17 | C2 |
| LCS | G ▷ C3×C72 | |
| UCS | C1 ◁ C2×C3×C17 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C17×C3⋊(C7⋊D7) | 2 |
| C2×C32×C72×C17 | 2 |
| C2×C3×C17×C7⋊D7 | 3 |
| C2×C17×C3⋊(C7⋊D7) | 3 |
| C2×C3×C17×D21 | 7 |
| C2×C3×C3⋊(C7⋊D7) | 17 |