Finite Group DatabasebetaFinite Group DatabasebetaOrder 27904.
338 conjugacy classes of subgroups; only the 74 normal subgroups are shown.
This group has 338 conjugacy classes of subgroups — too many to draw. Only its 74 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 | C109×#3199 | C2 |
| LCS | G ▷ C22×C8 ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C109 ◁ C22×C4×C109 ◁ #408×C109 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C109×#2233 | C2 | semidirect |
| 3. C109×#2232 | C2 | semidirect |
| 4. C109×#2078 | C2 | semidirect |
| 5. C109×#1349 | C2 | semidirect |
| 6. C109×#1349 | C2 | semidirect |
| 7. C109×#1315 | C2 | semidirect |
| 16. C2×#107×C109 | C22 | semidirect |
| 23. C22⋊C16×C109 | C22 | semidirect |
| 24. C22⋊C16×C109 | C22 | semidirect |
| 26. #341×C109 | C22 | semidirect |
| 156. #12284 | C109 | direct (N × H) |
| 165. #2233 | C2×C109 | semidirect |
| 166. #2232 | C2×C109 | semidirect |
| 167. #2078 | C2×C109 | semidirect |
| 168. #1349 | C2×C109 | semidirect |
| 169. #1349 | C2×C109 | semidirect |
| 170. #1315 | C2×C109 | semidirect |
| 171. C109 | #12284 | direct (N × H) |
| 180. C2×#107 | C22×C109 | semidirect |
| 187. C22⋊C16 | C22×C109 | semidirect |
| 188. C22⋊C16 | C22×C109 | semidirect |
| 190. #341 | C22×C109 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C109×#3199 | 2 |
| C109×#2233 | 2 |
| C109×#2232 | 2 |
| C109×#2078 | 2 |
| C109×#1349 | 2 |
| C109×#1315 | 2 |
| #12284 | 109 |