Finite Group DatabasebetaFinite Group DatabasebetaOrder 17792.
256 conjugacy classes of subgroups; only the 108 normal subgroups are shown.
This group has 256 conjugacy classes of subgroups — too many to draw. Only its 108 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C139 | C22⋊C4 |
| commutator | C2×C4 | C22×C4×C139 |
| Frattini, cosocle | C42 | C23×C139 |
| socle | C22×C139 | C2×C22⋊C4 |
| prime radical | #532×C139 | C2 |
| LCS | G ▷ C2×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C139 ◁ C2×C42×C139 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #431×C139 | C2 | semidirect |
| 3. C2×C4⋊C8×C139 | C2 | semidirect |
| 4. #332×C139 | C2 | semidirect |
| 5. #331×C139 | C2 | semidirect |
| 86. C139 | #1540 | direct (N × H) |
| 87. #1540 | C139 | direct (N × H) |
| 89. #431 | C2×C139 | semidirect |
| 90. C2×C4⋊C8 | C2×C139 | semidirect |
| 91. #332 | C2×C139 | semidirect |
| 92. #331 | C2×C139 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #532×C139 | 2 |
| #431×C139 | 2 |
| C2×C4⋊C8×C139 | 2 |
| #332×C139 | 2 |
| #331×C139 | 2 |
| #1540 | 139 |