Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
1502 conjugacy classes of subgroups; only the 1294 normal subgroups are shown.
This group has 1502 conjugacy classes of subgroups — too many to draw. Only its 1294 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C22×C4×C67 | C24 |
| commutator | C2 | C2×C43×C67 |
| Frattini, cosocle | C22×C4 | C24×C67 |
| socle | C23×C67 | C23×C4 |
| prime radical | C24×C67 | C22×C4 |
| LCS | G ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C4×C67 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. C67×#1726 | C2 | semidirect |
| 6. C4×M16×C67 | C4 | semidirect |
| 19. #97×C67 | C2×C4 | semidirect |
| 20. C4×C8×C67 | C2×C4 | semidirect |
| 51. #20329 | C67 | direct (N × H) |
| 57. #1726 | C2×C67 | semidirect |
| 58. C67 | #20329 | direct (N × H) |
| 61. C4×M16 | C4×C67 | semidirect |
| 74. #97 | C2×C4×C67 | semidirect |
| 75. C4×C8 | C2×C4×C67 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×M16×C67 | 2 |
| C2×#376×C67 | 2 |
| C67×#1726 | 2 |
| #20329 | 67 |