Finite Group DatabasebetaFinite Group DatabasebetaOrder 13952.
334 conjugacy classes of subgroups; only the 112 normal subgroups are shown.
This group has 334 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 | #120 |
| 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. #419×C109 | C2 | semidirect |
| 5. #391×C109 | C2 | semidirect |
| 6. #343×C109 | C2 | semidirect |
| 7. #339×C109 | C2 | semidirect |
| 11. #137×C109 | C4 | semidirect |
| 37. C2×Q8×C109 | C2×C4 | semidirect |
| 52. M16×C109 | C2×C4 | semidirect |
| 124. #1882 | C109 | direct (N × H) |
| 125. C109 | #1882 | direct (N × H) |
| 129. #419 | C2×C109 | semidirect |
| 130. #391 | C2×C109 | semidirect |
| 131. #343 | C2×C109 | semidirect |
| 132. #339 | C2×C109 | semidirect |
| 136. #137 | C4×C109 | semidirect |
| 162. C2×Q8 | C2×C4×C109 | semidirect |
| 177. M16 | C2×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 |
| #520×C109 | 2 |
| C2×#104×C109 | 2 |
| #419×C109 | 2 |
| #391×C109 | 2 |
| #343×C109 | 2 |
| #339×C109 | 2 |
| #1882 | 109 |