Finite Group DatabasebetaFinite Group DatabasebetaOrder 27392.
142 conjugacy classes of subgroups; only the 30 normal subgroups are shown.
This group has 142 conjugacy classes of subgroups — too many to draw. Only its 30 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C107 | #1408 |
| commutator | C4×C8 | C2×C4×C107 |
| Frattini, cosocle | #492 | C22×C107 |
| prime radical | #127×C107 | D4 |
| LCS | G ▷ C4×C8 ▷ C42 ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C107 ◁ C22×C107 ◁ C2×C4×C107 ◁ C42×C107 ◁ #492×C107 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 5. #494×C107 | C4 | semidirect |
| 10. #322×C107 | C4 | semidirect |
| 57. #7528 | C107 | direct (N × H) |
| 64. C107 | #7528 | direct (N × H) |
| 66. #494 | C4×C107 | semidirect |
| 71. #322 | C4×C107 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C107×#1722 | 2 |
| C107×#1410 | 2 |
| C107×#1409 | 2 |
| #7528 | 107 |