Finite Group DatabasebetaFinite Group DatabasebetaOrder 27904.
1390 conjugacy classes of subgroups; only the 622 normal subgroups are shown.
This group has 1390 conjugacy classes of subgroups — too many to draw. Only its 622 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 | C22 | C22×C42×C109 |
| Frattini, cosocle | C24 | C24×C109 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C24×C109 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 8. #391×C109 | C4 | semidirect |
| 33. C2×Q8×C109 | C42 | semidirect |
| 85. #13834 | C109 | direct (N × H) |
| 94. C109 | #13834 | direct (N × H) |
| 99. #391 | C4×C109 | semidirect |
| 124. C2×Q8 | C42×C109 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#391×C109 | 2 |
| C109×#1436 | 2 |
| C109×#1434 | 2 |
| #13834 | 109 |