Finite Group DatabasebetaFinite Group DatabasebetaOrder 28928.
320 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 320 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×C113 | #447 |
| commutator, Frattini, cosocle | C4×C8 | C23×C113 |
| prime radical | C113×#3403 | C2 |
| LCS | G ▷ C4×C8 ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C113 ◁ C42×C113 ◁ #446×C113 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C113×#2251 | C2 | semidirect |
| 3. C113×#2208 | C2 | semidirect |
| 4. C113×#1690 | C2 | semidirect |
| 5. C113×#1360 | C2 | semidirect |
| 6. C113×#1338 | C2 | semidirect |
| 7. C113×#1333 | C2 | semidirect |
| 149. #12338 | C113 | direct (N × H) |
| 156. #2251 | C2×C113 | semidirect |
| 157. #2208 | C2×C113 | semidirect |
| 158. #1690 | C2×C113 | semidirect |
| 159. #1360 | C2×C113 | semidirect |
| 160. #1338 | C2×C113 | semidirect |
| 161. #1333 | C2×C113 | semidirect |
| 162. C113 | #12338 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C113×#3403 | 2 |
| C113×#2251 | 2 |
| C113×#2208 | 2 |
| C113×#1690 | 2 |
| C113×#1360 | 2 |
| C113×#1338 | 2 |
| C113×#1333 | 2 |
| #12338 | 113 |