Finite Group DatabasebetaFinite Group DatabasebetaOrder 27904.
316 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 316 conjugacy classes of subgroups — too many to draw. Only its 78 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 | #447 |
| commutator, Frattini, cosocle | C22×C8 | C23×C109 |
| prime radical | #466×C109 | C22 |
| LCS | G ▷ C22×C8 ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C109 ◁ C22×C4×C109 ◁ C2×C4⋊C8×C109 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C109×#2235 | C2 | semidirect |
| 4. C109×#2086 | C2 | semidirect |
| 5. C109×#1348 | C2 | semidirect |
| 7. C109×#1322 | C2 | semidirect |
| 146. #12290 | C109 | direct (N × H) |
| 154. #2235 | C2×C109 | semidirect |
| 156. #2086 | C2×C109 | semidirect |
| 157. #1348 | C2×C109 | semidirect |
| 159. #1322 | C2×C109 | semidirect |
| 160. C109 | #12290 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C109×#3250 | 2 |
| C109×#2235 | 2 |
| C109×#2232 | 2 |
| C109×#2086 | 2 |
| C109×#1348 | 2 |
| C109×#1347 | 2 |
| C109×#1322 | 2 |
| #12290 | 109 |