Finite Group DatabasebetaFinite Group DatabasebetaOrder 13952.
232 conjugacy classes of subgroups; only the 96 normal subgroups are shown.
This group has 232 conjugacy classes of subgroups — too many to draw. Only its 96 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×C109 | #121 |
| commutator | C2×C4 | C22×C4×C109 |
| Frattini, cosocle | C22×C4 | C23×C109 |
| prime radical | C22×D4×C109 | C22 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C109 ◁ C22×C4×C109 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #428×C109 | C2 | semidirect |
| 5. #405×C109 | C2 | semidirect |
| 6. #343×C109 | C2 | semidirect |
| 7. #341×C109 | C2 | semidirect |
| 21. #100×C109 | C4 | semidirect |
| 100. #1931 | C109 | direct (N × H) |
| 101. C109 | #1931 | direct (N × H) |
| 102. #428 | C2×C109 | semidirect |
| 106. #405 | C2×C109 | semidirect |
| 107. #343 | C2×C109 | semidirect |
| 108. #341 | C2×C109 | semidirect |
| 122. #100 | C4×C109 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #428×C109 | 2 |
| #418×C109 | 2 |
| C2×#102×C109 | 2 |
| C2×#100×C109 | 2 |
| #405×C109 | 2 |
| #343×C109 | 2 |
| #341×C109 | 2 |
| #1931 | 109 |