Finite Group DatabasebetaFinite Group DatabasebetaOrder 35584.
668 conjugacy classes of subgroups; only the 98 normal subgroups are shown.
This group has 668 conjugacy classes of subgroups — too many to draw. Only its 98 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C139 | #120 |
| commutator, Frattini, cosocle | C2×C42 | C23×C139 |
| LCS | G ▷ C2×C42 ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C23×C139 ◁ C2×C42×C139 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #2733×C139 | C2 | semidirect |
| 2. #2014×C139 | C2 | semidirect |
| 3. #2011×C139 | C2 | semidirect |
| 4. #1272×C139 | C2 | semidirect |
| 5. #1270×C139 | C2 | semidirect |
| 53. C2×Q8×C139 | D8 | semidirect |
| 174. #7742 | C139 | direct (N × H) |
| 175. C139 | #7742 | direct (N × H) |
| 176. #2733 | C2×C139 | semidirect |
| 177. #2014 | C2×C139 | semidirect |
| 178. #2011 | C2×C139 | semidirect |
| 179. #1272 | C2×C139 | semidirect |
| 180. #1270 | C2×C139 | semidirect |
| 228. C2×Q8 | D8×C139 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #2733×C139 | 2 |
| #2014×C139 | 2 |
| #2011×C139 | 2 |
| #1272×C139 | 2 |
| #1270×C139 | 2 |
| #7742 | 139 |