Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
160 conjugacy classes of subgroups; only the 68 normal subgroups are shown.
This group has 160 conjugacy classes of subgroups — too many to draw. Only its 68 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 | #121 |
| commutator, Frattini, cosocle | C42 | C23×C137 |
| prime radical | C2×D4×C137 | D4 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C137 ◁ C42×C137 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #498×C137 | C2 | semidirect |
| 5. #335×C137 | C2 | semidirect |
| 6. #333×C137 | C2 | semidirect |
| 7. #332×C137 | C2 | semidirect |
| 59. C8×C137 | SD16 | semidirect |
| 76. C137 | #1691 | direct (N × H) |
| 77. #1691 | C137 | direct (N × H) |
| 78. #498 | C2×C137 | semidirect |
| 82. #335 | C2×C137 | semidirect |
| 83. #333 | C2×C137 | semidirect |
| 84. #332 | C2×C137 | semidirect |
| 136. C8 | SD16×C137 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #498×C137 | 2 |
| #476×C137 | 2 |
| #461×C137 | 2 |
| #436×C137 | 2 |
| #335×C137 | 2 |
| #333×C137 | 2 |
| #332×C137 | 2 |
| #1691 | 137 |