Finite Group DatabasebetaFinite Group DatabasebetaOrder 7552.
166 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 166 conjugacy classes of subgroups — too many to draw. Only its 69 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C2×C4 | C2×D236 |
| commutator | C2×C4×C59 | C22×C4 |
| Frattini | C42 | C22×D59 |
| Fitting | C82×C59 | C2 |
| socle | C22×C59 | C4×D4 |
| hypercenter | C82 | D59 |
| hypocenter | C59 | #1590 |
| LCS | G ▷ C2×C4×C59 ▷ C2×C59 ▷ C59 | |
| UCS | C1 ◁ C2×C4 ◁ C4×C8 ◁ C82 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #16837532 | C2 | semidirect |
| 4. #16837153 | C2 | semidirect |
| 5. #16837134 | C2 | semidirect |
| 7. C82×C59 | C2 | semidirect |
| 57. C8×C59 | M16 | semidirect |
| 58. C8×C59 | SD16 | semidirect |
| 84. C82 | D59 | semidirect |
| 85. C59 | #1590 | semidirect |
| 137. C8 | #11745659 | semidirect |
| 138. C8 | #11745660 | semidirect |