Finite Group DatabasebetaFinite Group DatabasebetaOrder 8768.
124 conjugacy classes of subgroups; only the 48 normal subgroups are shown.
This group has 124 conjugacy classes of subgroups — too many to draw. Only its 48 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 | C2×D4×C137 | C4 |
| hypercenter | C2×D4 | #10587739 |
| hypocenter | C137 | #435 |
| LCS | G ▷ C22×C137 ▷ C137 | |
| UCS | C1 ◁ C22 ◁ C2×D4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#14555519 | C2 | semidirect |
| 2. C22×#11764047 | C2 | semidirect |
| 3. #17984155 | C2 | semidirect |
| 4. C22⋊#11764047 | C2 | semidirect |
| 5. C22⋊#11764047 | C2 | semidirect |
| 6. #17984143 | C2 | semidirect |
| 24. #11764047 | D4 | semidirect |
| 42. C22×C137 | M16 | semidirect |
| 55. C137 | #435 | semidirect |
| 98. C22 | #14555519 | semidirect |