Finite Group DatabasebetaFinite Group DatabasebetaOrder 27904.
500 conjugacy classes of subgroups; only the 134 normal subgroups are shown.
This group has 500 conjugacy classes of subgroups — too many to draw. Only its 134 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×D4×C109 | C2×C4 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C109 ◁ C22×C4×C109 ◁ C2×C4×Q8×C109 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. C109×#1801 | C2 | semidirect |
| 4. C109×#1394 | C2 | semidirect |
| 144. C4×C109 | #355 | semidirect |
| 145. #12801 | C109 | direct (N × H) |
| 154. #1801 | C2×C109 | semidirect |
| 155. #1394 | C2×C109 | semidirect |
| 156. C109 | #12801 | direct (N × H) |
| 296. C4 | #355×C109 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#124×C109 | 2 |
| C2×#355×C109 | 2 |
| C109×#1801 | 2 |
| C109×#1394 | 2 |
| #12801 | 109 |