Finite Group DatabasebetaFinite Group DatabasebetaOrder 13952.
312 conjugacy classes of subgroups; only the 112 normal subgroups are shown.
This group has 312 conjugacy classes of subgroups — too many to draw. Only its 112 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 | C2×#41×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 |
|---|---|---|
| 4. C2×#103×C109 | C2 | semidirect |
| 5. C2×#101×C109 | C2 | semidirect |
| 6. #343×C109 | C2 | semidirect |
| 7. #341×C109 | C2 | semidirect |
| 11. #137×C109 | C4 | semidirect |
| 116. #1908 | C109 | direct (N × H) |
| 117. C109 | #1908 | direct (N × H) |
| 121. C2×#103 | C2×C109 | semidirect |
| 122. C2×#101 | C2×C109 | semidirect |
| 123. #343 | C2×C109 | semidirect |
| 124. #341 | C2×C109 | semidirect |
| 128. #137 | C4×C109 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#137×C109 | 2 |
| C2×#131×C109 | 2 |
| #417×C109 | 2 |
| C2×#103×C109 | 2 |
| C2×#101×C109 | 2 |
| #343×C109 | 2 |
| #341×C109 | 2 |
| #1908 | 109 |