Finite Group DatabasebetaFinite Group DatabasebetaOrder 7232.
120 conjugacy classes of subgroups; only the 70 normal subgroups are shown.
This group has 120 conjugacy classes of subgroups — too many to draw. Only its 70 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×C113 | C2×D4 |
| commutator | C4 | C22×C4×C113 |
| Frattini, cosocle | C2×C4 | C23×C113 |
| prime radical | C2×D4×C113 | C22 |
| LCS | G ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C113 ◁ C42×C113 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C4×Q8×C113 | C2 | semidirect |
| 4. #107×C113 | C2 | semidirect |
| 5. #103×C113 | C2 | semidirect |
| 7. #97×C113 | C2 | semidirect |
| 11. SD16×C113 | C4 | semidirect |
| 22. Q8×C113 | C2×C4 | semidirect |
| 33. C8×C113 | C2×C4 | semidirect |
| 49. C113 | #440 | direct (N × H) |
| 50. #440 | C113 | direct (N × H) |
| 52. C4×Q8 | C2×C113 | semidirect |
| 54. #107 | C2×C113 | semidirect |
| 55. #103 | C2×C113 | semidirect |
| 57. #97 | C2×C113 | semidirect |
| 61. SD16 | C4×C113 | semidirect |
| 72. Q8 | C2×C4×C113 | semidirect |
| 83. C8 | C2×C4×C113 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×SD16×C113 | 2 |
| C4×Q8×C113 | 2 |
| C4×D4×C113 | 2 |
| #107×C113 | 2 |
| #103×C113 | 2 |
| #102×C113 | 2 |
| #97×C113 | 2 |
| #440 | 113 |