Finite Group DatabasebetaFinite Group DatabasebetaOrder 27392.
656 conjugacy classes of subgroups; only the 238 normal subgroups are shown.
This group has 656 conjugacy classes of subgroups — too many to draw. Only its 238 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×C107 | C22×D4 |
| commutator, Frattini, cosocle | C22×C4 | C24×C107 |
| prime radical | C22×D4×C107 | C23 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C107 ◁ #376×C107 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C107×#2645 | C2 | semidirect |
| 4. C107×#1941 | C2 | semidirect |
| 6. C107×#1935 | C2 | semidirect |
| 7. C107×#1726 | C2 | semidirect |
| 111. #33271 | C107 | direct (N × H) |
| 116. #2645 | C2×C107 | semidirect |
| 119. #1941 | C2×C107 | semidirect |
| 121. #1935 | C2×C107 | semidirect |
| 122. #1726 | C2×C107 | semidirect |
| 123. C107 | #33271 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C107×#2645 | 2 |
| C107×#2644 | 2 |
| C107×#1968 | 2 |
| C107×#1941 | 2 |
| C107×#1936 | 2 |
| C107×#1935 | 2 |
| C107×#1726 | 2 |
| #33271 | 107 |