Finite Group DatabasebetaFinite Group DatabasebetaOrder 27392.
284 conjugacy classes of subgroups; only the 94 normal subgroups are shown.
This group has 284 conjugacy classes of subgroups — too many to draw. Only its 94 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 | #1530 |
| commutator | C42 | C22×C4×C107 |
| Frattini, cosocle | #97 | C23×C107 |
| prime radical | #540×C107 | C4 |
| LCS | G ▷ C42 ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C107 ◁ C2×C4×C107 ◁ #405×C107 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C107×#2166 | C2 | semidirect |
| 3. C107×#2110 | C2 | semidirect |
| 4. C107×#1356 | C2 | semidirect |
| 5. C107×#1355 | C2 | semidirect |
| 124. #11912 | C107 | direct (N × H) |
| 130. #2166 | C2×C107 | semidirect |
| 131. #2110 | C2×C107 | semidirect |
| 132. #1356 | C2×C107 | semidirect |
| 133. #1355 | C2×C107 | semidirect |
| 134. C107 | #11912 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C107×#3174 | 2 |
| C107×#2166 | 2 |
| C107×#2110 | 2 |
| C107×#1356 | 2 |
| C107×#1355 | 2 |
| #11912 | 107 |