Finite Group DatabasebetaFinite Group DatabasebetaOrder 27392.
332 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 332 conjugacy classes of subgroups — too many to draw. Only its 86 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 | #2127 |
| commutator | C42 | C22×C4×C107 |
| Frattini, cosocle | #124 | C23×C107 |
| prime radical | #535×C107 | C22 |
| LCS | G ▷ C42 ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C107 ◁ C22×C107 ◁ C22×C4×C107 ◁ #535×C107 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 4. C107×#1414 | C2 | semidirect |
| 5. C107×#1407 | C2 | semidirect |
| 6. #541×C107 | C4 | semidirect |
| 9. #492×C107 | C4 | semidirect |
| 10. #490×C107 | C4 | semidirect |
| 16. #433×C107 | C4 | semidirect |
| 30. C4⋊Q8×C107 | C2×C4 | semidirect |
| 35. #125×C107 | C2×C4 | semidirect |
| 54. #97×C107 | C2×C4 | semidirect |
| 55. C4×C8×C107 | C2×C4 | semidirect |
| 146. #13607 | C107 | direct (N × H) |
| 156. #1414 | C2×C107 | semidirect |
| 157. #1407 | C2×C107 | semidirect |
| 158. C107 | #13607 | direct (N × H) |
| 159. #541 | C4×C107 | semidirect |
| 162. #492 | C4×C107 | semidirect |
| 163. #490 | C4×C107 | semidirect |
| 169. #433 | C4×C107 | semidirect |
| 183. C4⋊Q8 | C2×C4×C107 | semidirect |
| 188. #125 | C2×C4×C107 | semidirect |
| 207. #97 | C2×C4×C107 | semidirect |
| 208. C4×C8 | C2×C4×C107 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C107×#3222 | 2 |
| C107×#2134 | 2 |
| C107×#2127 | 2 |
| C107×#1414 | 2 |
| C107×#1407 | 2 |
| #13607 | 107 |