Finite Group DatabasebetaFinite Group DatabasebetaOrder 27904.
962 conjugacy classes of subgroups; only the 150 normal subgroups are shown.
This group has 962 conjugacy classes of subgroups — too many to draw. Only its 150 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×C109 | C2×#99 |
| commutator | C22×C4 | C22×C4×C109 |
| Frattini, cosocle | C22×Q8 | C23×C109 |
| prime radical | C22×#41×C109 | C4 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C109 ◁ C24×C109 ◁ C23×Q8×C109 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×#356×C109 | C2 | semidirect |
| 3. C2×#355×C109 | C2 | semidirect |
| 4. C109×#1784 | C2 | semidirect |
| 185. #12702 | C109 | direct (N × H) |
| 193. C2×#356 | C2×C109 | semidirect |
| 194. C2×#355 | C2×C109 | semidirect |
| 195. #1784 | C2×C109 | semidirect |
| 196. C109 | #12702 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#536×C109 | 2 |
| C2×#356×C109 | 2 |
| C2×#355×C109 | 2 |
| C109×#1784 | 2 |
| #12702 | 109 |