Finite Group DatabasebetaFinite Group DatabasebetaOrder 14464.
436 conjugacy classes of subgroups; only the 188 normal subgroups are shown.
This group has 436 conjugacy classes of subgroups — too many to draw. Only its 188 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 | C22×D4 |
| commutator, Frattini, cosocle | C2×C4 | C24×C113 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C113 ◁ C2×C42×C113 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #532×C113 | C2 | semidirect |
| 2. #474×C113 | C2 | semidirect |
| 3. #466×C113 | C2 | semidirect |
| 4. #459×C113 | C2 | semidirect |
| 5. C2×C4⋊C8×C113 | C2 | semidirect |
| 52. C2×C4×C113 | D8 | semidirect |
| 76. #3245 | C113 | direct (N × H) |
| 77. C113 | #3245 | direct (N × H) |
| 78. #532 | C2×C113 | semidirect |
| 79. #474 | C2×C113 | semidirect |
| 80. #466 | C2×C113 | semidirect |
| 81. #459 | C2×C113 | semidirect |
| 82. C2×C4⋊C8 | C2×C113 | semidirect |
| 129. C2×C4 | D8×C113 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #532×C113 | 2 |
| #474×C113 | 2 |
| #466×C113 | 2 |
| #459×C113 | 2 |
| C2×C4⋊C8×C113 | 2 |
| #3245 | 113 |