Finite Group DatabasebetaFinite Group DatabasebetaOrder 27392.
206 conjugacy classes of subgroups; only the 142 normal subgroups are shown.
This group has 206 conjugacy classes of subgroups — too many to draw. Only its 142 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C23×C107 | D16 |
| commutator | C16 | C22×C4×C107 |
| Frattini, cosocle | C2×C16 | C23×C107 |
| LCS | G ▷ C16 ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C107 ◁ C22×C4×C107 ◁ C22×C8×C107 ◁ C22×C16×C107 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. C107×#1424 | C2 | direct (N × H) |
| 6. C2×C32×C107 | C4 | semidirect |
| 18. C32×C107 | C2×C4 | semidirect |
| 47. C2×#1424 | C107 | direct (N × H) |
| 48. C2×C107 | #1424 | direct (N × H) |
| 53. #1424 | C2×C107 | direct (N × H) |
| 54. C107 | C2×#1424 | direct (N × H) |
| 57. C2×C32 | C4×C107 | semidirect |
| 69. C32 | C2×C4×C107 | semidirect |
| 98. C2 | C107×#1424 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C32×C107 | 2 |
| C2×#366×C107 | 2 |
| C107×#1424 | 2 |
| C2×#1424 | 107 |