Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
1182 conjugacy classes of subgroups; only the 462 normal subgroups are shown.
This group has 1182 conjugacy classes of subgroups — too many to draw. Only its 462 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C24×C67 | C24 |
| commutator | C23 | C23×C4×C67 |
| Frattini, cosocle | C24 | C24×C67 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C24×C67 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 7. #384×C67 | C4 | semidirect |
| 37. C42×C67 | C4⋊C4 | semidirect |
| 64. #14676 | C67 | direct (N × H) |
| 73. C67 | #14676 | direct (N × H) |
| 77. #384 | C4×C67 | semidirect |
| 107. C42 | C4⋊C4×C67 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#384×C67 | 2 |
| C2×#383×C67 | 2 |
| C67×#1441 | 2 |
| #14676 | 67 |