Finite Group DatabasebetaFinite Group DatabasebetaOrder 28928.
168 conjugacy classes of subgroups; only the 70 normal subgroups are shown.
This group has 168 conjugacy classes of subgroups — too many to draw. Only its 70 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 | C2×D16 |
| commutator, Frattini, cosocle | C2×C16 | C23×C113 |
| prime radical | C23×C113 | D16 |
| LCS | G ▷ C2×C16 ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C113 ◁ C22×C4×C113 ◁ C22×C8×C113 ◁ C22×C16×C113 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. C113×#1424 | C2 | semidirect |
| 4. C113×#1423 | C2 | semidirect |
| 5. C113×#1416 | C2 | semidirect |
| 6. C113×#1416 | C2 | semidirect |
| 79. #13716 | C113 | direct (N × H) |
| 86. #1424 | C2×C113 | semidirect |
| 87. #1423 | C2×C113 | semidirect |
| 88. #1416 | C2×C113 | semidirect |
| 89. #1416 | C2×C113 | semidirect |
| 91. C113 | #13716 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C113×#2216 | 2 |
| C113×#2158 | 2 |
| C113×#1424 | 2 |
| C113×#1423 | 2 |
| C113×#1416 | 2 |
| C113×C22⋊C32 | 2 |
| #13716 | 113 |