Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
186 conjugacy classes of subgroups; only the 118 normal subgroups are shown.
This group has 186 conjugacy classes of subgroups — too many to draw. Only its 118 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C32×C47 | D4 |
| commutator | C4 | C22×C16×C47 |
| Frattini, cosocle | C2×C16 | C23×C47 |
| socle | C2×C47 | D4×C16 |
| prime radical | #135×C47 | C8 |
| LCS | G ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C32×C47 ◁ C2×C32×C47 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C47×#2258 | C2 | semidirect |
| 3. C47×#1422 | C2 | semidirect |
| 4. C47×#1401 | C2 | semidirect |
| 5. C4×C32×C47 | C2 | semidirect |
| 55. #13647 | C47 | direct (N × H) |
| 62. #2258 | C2×C47 | semidirect |
| 64. #1422 | C2×C47 | semidirect |
| 65. #1401 | C2×C47 | semidirect |
| 66. C4×C32 | C2×C47 | semidirect |
| 80. C47 | #13647 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C47×#2258 | 2 |
| C47×#2170 | 2 |
| C47×#1422 | 2 |
| C47×#1401 | 2 |
| C4×C32×C47 | 2 |
| #13647 | 47 |