Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
504 conjugacy classes of subgroups; only the 112 normal subgroups are shown.
This group has 504 conjugacy classes of subgroups — too many to draw. Only its 112 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C137 | C2×C22⋊C4 |
| commutator | C23 | C22×C4×C137 |
| Frattini, cosocle | C24 | C23×C137 |
| prime radical | C25×C137 | C22 |
| LCS | G ▷ C23 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C137 ◁ C25×C137 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. #342×C137 | C2 | semidirect |
| 5. C23×C4×C137 | C4 | semidirect |
| 8. C2×C22⋊C4×C137 | C4 | semidirect |
| 68. C137 | #1819 | direct (N × H) |
| 69. #1819 | C137 | direct (N × H) |
| 72. #342 | C2×C137 | semidirect |
| 74. C23×C4 | C4×C137 | semidirect |
| 77. C2×C22⋊C4 | C4×C137 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C22⋊C4×C137 | 2 |
| #379×C137 | 2 |
| #342×C137 | 2 |
| #1819 | 137 |