Finite Group DatabasebetaFinite Group DatabasebetaOrder 27904.
372 conjugacy classes of subgroups; only the 82 normal subgroups are shown.
This group has 372 conjugacy classes of subgroups — too many to draw. Only its 82 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 | C4×C8 | C23×C109 |
| prime radical | C109×#3273 | C2 |
| LCS | G ▷ C4×C8 ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C109 ◁ C42×C109 ◁ #436×C109 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C109×#2243 | C2 | semidirect |
| 3. C109×#2226 | C2 | semidirect |
| 4. C109×#1693 | C2 | semidirect |
| 5. C109×#1360 | C2 | semidirect |
| 6. C109×#1333 | C2 | semidirect |
| 7. C109×#1330 | C2 | semidirect |
| 10. #500×C109 | C22 | semidirect |
| 20. C4⋊C16×C109 | C22 | semidirect |
| 24. #346×C109 | C22 | semidirect |
| 25. #334×C109 | C22 | semidirect |
| 86. D8×C109 | SD16 | semidirect |
| 160. #12378 | C109 | direct (N × H) |
| 168. #2243 | C2×C109 | semidirect |
| 169. #2226 | C2×C109 | semidirect |
| 170. #1693 | C2×C109 | semidirect |
| 171. #1360 | C2×C109 | semidirect |
| 172. #1333 | C2×C109 | semidirect |
| 173. #1330 | C2×C109 | semidirect |
| 174. C109 | #12378 | direct (N × H) |
| 177. #500 | C22×C109 | semidirect |
| 187. C4⋊C16 | C22×C109 | semidirect |
| 191. #346 | C22×C109 | semidirect |
| 192. #334 | C22×C109 | semidirect |
| 253. D8 | SD16×C109 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C109×#3273 | 2 |
| C109×#2243 | 2 |
| C109×#2226 | 2 |
| C109×#1693 | 2 |
| C109×#1360 | 2 |
| C109×#1333 | 2 |
| C109×#1330 | 2 |
| #12378 | 109 |