Finite Group DatabasebetaFinite Group DatabasebetaOrder 35072.
528 conjugacy classes of subgroups; only the 218 normal subgroups are shown.
This group has 528 conjugacy classes of subgroups — too many to draw. Only its 218 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×D8 |
| commutator, Frattini, cosocle | C2×C8 | C24×C137 |
| prime radical | #3391×C137 | C2 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C137 ◁ C4×Q8×C137 ◁ C8×Q8×C137 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. Q8×Q16×C137 | C2 | semidirect |
| 3. #2240×C137 | C2 | semidirect |
| 4. #2226×C137 | C2 | semidirect |
| 5. #2207×C137 | C2 | semidirect |
| 6. Q8×C16×C137 | C2 | semidirect |
| 7. C4×SD32×C137 | C2 | semidirect |
| 55. Q16×C137 | #41 | semidirect |
| 75. Q8×C137 | SD32 | semidirect |
| 105. #33929 | C137 | direct (N × H) |
| 106. C137 | #33929 | direct (N × H) |
| 108. Q8×Q16 | C2×C137 | semidirect |
| 109. #2240 | C2×C137 | semidirect |
| 110. #2226 | C2×C137 | semidirect |
| 111. #2207 | C2×C137 | semidirect |
| 112. Q8×C16 | C2×C137 | semidirect |
| 113. C4×SD32 | C2×C137 | semidirect |
| 161. Q16 | #41×C137 | semidirect |
| 181. Q8 | SD32×C137 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #3391×C137 | 2 |
| Q8×Q16×C137 | 2 |
| #2240×C137 | 2 |
| #2226×C137 | 2 |
| #2207×C137 | 2 |
| Q8×C16×C137 | 2 |
| C4×SD32×C137 | 2 |
| #33929 | 137 |