Finite Group DatabasebetaFinite Group DatabasebetaOrder 8768.
190 conjugacy classes of subgroups; only the 58 normal subgroups are shown.
This group has 190 conjugacy classes of subgroups — too many to draw. Only its 58 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C22×#10587739 |
| commutator, socle | C22×C137 | C22×C4 |
| Fitting | C22×C4×C137 | C4 |
| hypercenter | C22×C4 | #10587739 |
| hypocenter | C137 | #407 |
| LCS | G ▷ C22×C137 ▷ C137 | |
| UCS | C1 ◁ C22 ◁ C22×C4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#14555520 | C2 | semidirect |
| 2. #17984145 | C2 | semidirect |
| 3. C22⋊#11764047 | C2 | semidirect |
| 6. C2×#11764047 | C22 | semidirect |
| 34. C22×C137 | M16 | semidirect |
| 42. C2×D137 | M16 | semidirect |
| 53. C137 | #407 | semidirect |
| 95. C22 | #14555520 | semidirect |