Finite Group DatabasebetaFinite Group DatabasebetaOrder 27904.
2278 conjugacy classes of subgroups; only the 590 normal subgroups are shown.
This group has 2278 conjugacy classes of subgroups — too many to draw. Only its 590 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×C109 | C24 |
| commutator, Frattini, cosocle | C24 | C24×C109 |
| LCS | G ▷ C24 ▷ C1 | |
| UCS | C1 ◁ C24×C109 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 30. #95×C109 | Q8 | semidirect |
| 73. C2×C4×C109 | C4⋊Q8 | semidirect |
| 85. #15190 | C109 | direct (N × H) |
| 95. C109 | #15190 | direct (N × H) |
| 121. #95 | Q8×C109 | semidirect |
| 164. C2×C4 | C4⋊Q8×C109 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C4⋊Q8×C109 | 2 |
| C2×#391×C109 | 2 |
| C109×#1444 | 2 |
| C4×#95×C109 | 2 |
| #15190 | 109 |