Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
392 conjugacy classes of subgroups; only the 184 normal subgroups are shown.
This group has 392 conjugacy classes of subgroups — too many to draw. Only its 184 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 | C22×D4 |
| commutator, Frattini, cosocle | C2×C4 | C24×C137 |
| prime radical | #532×C137 | C2 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ 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. C2×#125×C137 | C2 | semidirect |
| 3. #491×C137 | C2 | semidirect |
| 4. #490×C137 | C2 | semidirect |
| 5. #488×C137 | C2 | semidirect |
| 6. #417×C137 | C2 | semidirect |
| 7. C4×M16×C137 | C2 | semidirect |
| 77. C137 | #3142 | direct (N × H) |
| 78. #3142 | C137 | direct (N × H) |
| 80. C2×#125 | C2×C137 | semidirect |
| 81. #491 | C2×C137 | semidirect |
| 82. #490 | C2×C137 | semidirect |
| 83. #488 | C2×C137 | semidirect |
| 84. #417 | C2×C137 | semidirect |
| 85. C4×M16 | C2×C137 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #532×C137 | 2 |
| C2×#125×C137 | 2 |
| #491×C137 | 2 |
| #490×C137 | 2 |
| #488×C137 | 2 |
| #417×C137 | 2 |
| C4×M16×C137 | 2 |
| #3142 | 137 |