Finite Group DatabasebetaFinite Group DatabasebetaOrder 17792.
140 conjugacy classes of subgroups; only the 64 normal subgroups are shown.
This group has 140 conjugacy classes of subgroups — too many to draw. Only its 64 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×C139 | C2×D8 |
| commutator, Frattini, cosocle | C2×C8 | C23×C139 |
| prime radical | C23×C139 | D8 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C139 ◁ C22×C4×C139 ◁ C22×C8×C139 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. #366×C139 | C2 | semidirect |
| 4. #358×C139 | C2 | semidirect |
| 55. C139 | #2236 | direct (N × H) |
| 56. #2236 | C139 | direct (N × H) |
| 59. #366 | C2×C139 | semidirect |
| 60. #358 | C2×C139 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #467×C139 | 2 |
| C2×#107×C139 | 2 |
| #366×C139 | 2 |
| #358×C139 | 2 |
| C22⋊C16×C139 | 2 |
| #2236 | 139 |