Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
134 conjugacy classes of subgroups; only the 44 normal subgroups are shown.
This group has 134 conjugacy classes of subgroups — too many to draw. Only its 44 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×C107 | #99 |
| commutator | C2×C4 | C2×C8×C107 |
| Frattini, cosocle | C2×C4⋊C4 | C22×C107 |
| prime radical | C23×C107 | C22⋊C4 |
| LCS | G ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C107 ◁ C23×C107 ◁ C2×C4⋊C4×C107 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 11. C2×Q8×C107 | C8 | semidirect |
| 50. #1319 | C107 | direct (N × H) |
| 51. C107 | #1319 | direct (N × H) |
| 62. C2×Q8 | C8×C107 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #391×C107 | 2 |
| #324×C107 | 2 |
| #1319 | 107 |