Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
314 conjugacy classes of subgroups; only the 110 normal subgroups are shown.
This group has 314 conjugacy classes of subgroups — too many to draw. Only its 110 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×C47 | #329 |
| commutator | C42 | C22×C4×C47 |
| Frattini, cosocle | #97 | C23×C47 |
| prime radical | C23×C47 | #100 |
| LCS | G ▷ C42 ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C47 ◁ C22×C4×C47 ◁ C2×#97×C47 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. C47×#1356 | C2 | direct (N × H) |
| 73. C2×#1356 | C47 | direct (N × H) |
| 86. #1356 | C2×C47 | direct (N × H) |
| 89. C2×C47 | #1356 | direct (N × H) |
| 101. C47 | C2×#1356 | direct (N × H) |
| 173. C2 | C47×#1356 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C47×#491 | 2 |
| C2×C47×#347 | 2 |
| C47×#1356 | 2 |
| C2×#1356 | 47 |