Finite Group DatabasebetaFinite Group DatabasebetaOrder 27904.
662 conjugacy classes of subgroups; only the 206 normal subgroups are shown.
This group has 662 conjugacy classes of subgroups — too many to draw. Only its 206 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 | C23×C109 | C22×D4 |
| commutator, Frattini, cosocle | C22×C4 | C24×C109 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C109 ◁ #376×C109 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 76. #32816 | C109 | direct (N × H) |
| 85. C109 | #32816 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C109×#2642 | 2 |
| C109×#2056 | 2 |
| C109×#2026 | 2 |
| C109×#2016 | 2 |
| C109×#1832 | 2 |
| #32816 | 109 |