Finite Group DatabasebetaFinite Group DatabasebetaOrder 35072.
360 conjugacy classes of subgroups; only the 110 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 110 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 | #493 |
| commutator, Frattini, cosocle | C4×C8 | C23×C137 |
| LCS | G ▷ C4×C8 ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C137 ◁ C42×C137 ◁ C82×C137 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #2248×C137 | C2 | semidirect |
| 2. #2246×C137 | C2 | semidirect |
| 3. #1712×C137 | C2 | semidirect |
| 4. #1709×C137 | C2 | semidirect |
| 5. #1311×C137 | C2 | semidirect |
| 43. C16×C137 | D8 | semidirect |
| 69. #12519 | C137 | direct (N × H) |
| 70. C137 | #12519 | direct (N × H) |
| 71. #2248 | C2×C137 | semidirect |
| 72. #2246 | C2×C137 | semidirect |
| 73. #1712 | C2×C137 | semidirect |
| 74. #1709 | C2×C137 | semidirect |
| 75. #1311 | C2×C137 | semidirect |
| 113. C16 | D8×C137 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #2248×C137 | 2 |
| #2246×C137 | 2 |
| #1712×C137 | 2 |
| #1709×C137 | 2 |
| #1311×C137 | 2 |
| #12519 | 137 |