Finite Group DatabasebetaFinite Group DatabasebetaOrder 27392.
992 conjugacy classes of subgroups; only the 222 normal subgroups are shown.
This group has 992 conjugacy classes of subgroups — too many to draw. Only its 222 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×C107 | C2×#120 |
| commutator, Frattini, cosocle | C42 | C24×C107 |
| prime radical | C107×#3549 | C2 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C107 ◁ C2×C42×C107 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C107×#3216 | C2 | semidirect |
| 3. C107×#3135 | C2 | semidirect |
| 4. C107×#1659 | C2 | semidirect |
| 5. C107×#1536 | C2 | semidirect |
| 6. C107×#1530 | C2 | semidirect |
| 14. #533×C107 | C22 | semidirect |
| 17. #497×C107 | C22 | semidirect |
| 20. #489×C107 | C22 | semidirect |
| 21. #489×C107 | C22 | semidirect |
| 25. #432×C107 | C22 | semidirect |
| 27. C2×#97×C107 | C22 | semidirect |
| 28. #329×C107 | C22 | semidirect |
| 29. #329×C107 | C22 | semidirect |
| 165. #19056 | C107 | direct (N × H) |
| 172. #3216 | C2×C107 | semidirect |
| 173. #3135 | C2×C107 | semidirect |
| 174. #1659 | C2×C107 | semidirect |
| 175. #1536 | C2×C107 | semidirect |
| 176. #1530 | C2×C107 | semidirect |
| 177. C107 | #19056 | direct (N × H) |
| 185. #533 | C22×C107 | semidirect |
| 188. #497 | C22×C107 | semidirect |
| 191. #489 | C22×C107 | semidirect |
| 192. #489 | C22×C107 | semidirect |
| 196. #432 | C22×C107 | semidirect |
| 198. C2×#97 | C22×C107 | semidirect |
| 199. #329 | C22×C107 | semidirect |
| 200. #329 | C22×C107 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C107×#3549 | 2 |
| C107×#3216 | 2 |
| C107×#3135 | 2 |
| C107×#1659 | 2 |
| C107×#1536 | 2 |
| C107×#1530 | 2 |
| #19056 | 107 |