Finite Group DatabasebetaFinite Group DatabasebetaOrder 28928.
700 conjugacy classes of subgroups; only the 118 normal subgroups are shown.
This group has 700 conjugacy classes of subgroups — too many to draw. Only its 118 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 | B(4,𝔽2) |
| commutator | C2×Q8 | C22×C4×C113 |
| Frattini, cosocle | C22×Q8 | C23×C113 |
| prime radical | C2×#454×C113 | C2 |
| LCS | G ▷ C2×Q8 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C113 ◁ C23×C113 ◁ C22×Q8×C113 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C113×#2372 | C2 | semidirect |
| 3. C2×#355×C113 | C2 | semidirect |
| 4. C113×#1793 | C2 | semidirect |
| 5. C113×#1394 | C2 | semidirect |
| 10. #454×C113 | C4 | semidirect |
| 25. 2−1+4×C113 | C2×C4 | semidirect |
| 56. #101×C113 | C2×C4 | semidirect |
| 181. #13057 | C113 | direct (N × H) |
| 189. #2372 | C2×C113 | semidirect |
| 190. C2×#355 | C2×C113 | semidirect |
| 191. #1793 | C2×C113 | semidirect |
| 192. #1394 | C2×C113 | semidirect |
| 193. C113 | #13057 | direct (N × H) |
| 198. #454 | C4×C113 | semidirect |
| 213. 2−1+4 | C2×C4×C113 | semidirect |
| 244. #101 | C2×C4×C113 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#454×C113 | 2 |
| C113×#2372 | 2 |
| C2×#355×C113 | 2 |
| C113×#1793 | 2 |
| C113×#1394 | 2 |
| #13057 | 113 |