Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
344 conjugacy classes of subgroups; only the 112 normal subgroups are shown.
This group has 344 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 | C2×C4 | C22×C4×C137 |
| Frattini, cosocle | C42 | C23×C137 |
| prime radical | C2×#127×C137 | C2 |
| LCS | G ▷ C2×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C137 ◁ C2×C42×C137 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #431×C137 | C2 | semidirect |
| 3. #423×C137 | C2 | semidirect |
| 4. #331×C137 | C2 | semidirect |
| 15. C4⋊C8×C137 | C22 | semidirect |
| 16. C4⋊C8×C137 | C22 | semidirect |
| 84. C137 | #1545 | direct (N × H) |
| 85. #1545 | C137 | direct (N × H) |
| 87. #431 | C2×C137 | semidirect |
| 88. #423 | C2×C137 | semidirect |
| 89. #331 | C2×C137 | semidirect |
| 100. C4⋊C8 | C22×C137 | semidirect |
| 101. C4⋊C8 | C22×C137 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#127×C137 | 2 |
| #431×C137 | 2 |
| #423×C137 | 2 |
| #331×C137 | 2 |
| #1545 | 137 |