Finite Group DatabasebetaFinite Group DatabasebetaOrder 27392.
1250 conjugacy classes of subgroups; only the 350 normal subgroups are shown.
This group has 1250 conjugacy classes of subgroups — too many to draw. Only its 350 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C24×C107 | C24 |
| commutator, Frattini, cosocle | C24 | C24×C107 |
| LCS | G ▷ C24 ▷ C1 | |
| UCS | C1 ◁ C24×C107 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 20. C2×C4⋊C4×C107 | Q8 | semidirect |
| 80. #16248 | C107 | direct (N × H) |
| 89. C107 | #16248 | direct (N × H) |
| 106. C2×C4⋊C4 | Q8×C107 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C107×#1446 | 2 |
| C107×#1445 | 2 |
| C107×#1436 | 2 |
| #16248 | 107 |