Finite Group DatabasebetaFinite Group DatabasebetaOrder 27392.
492 conjugacy classes of subgroups; only the 106 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 106 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×C107 | #392 |
| commutator, Frattini, cosocle | C2×C42 | C23×C107 |
| prime radical | #532×C107 | C22 |
| LCS | G ▷ C2×C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C107 ◁ C2×C42×C107 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. C107×#3165 | C2 | semidirect |
| 4. C107×#1966 | C2 | semidirect |
| 6. C107×#1485 | C2 | semidirect |
| 7. C107×#1299 | C2 | semidirect |
| 174. #10116 | C107 | direct (N × H) |
| 182. #3165 | C2×C107 | semidirect |
| 183. #1966 | C2×C107 | semidirect |
| 185. #1485 | C2×C107 | semidirect |
| 186. #1299 | C2×C107 | semidirect |
| 187. C107 | #10116 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C107×#3254 | 2 |
| C107×#3227 | 2 |
| C107×#3165 | 2 |
| C107×#1966 | 2 |
| C107×#1525 | 2 |
| C107×#1485 | 2 |
| C107×#1299 | 2 |
| #10116 | 107 |