Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
1386 conjugacy classes of subgroups; only the 366 normal subgroups are shown.
This group has 1386 conjugacy classes of subgroups — too many to draw. Only its 366 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C67 | C22×D4 |
| commutator, Frattini, cosocle | C22×C4 | C24×C67 |
| prime radical | C67×#2867 | C2 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C67 ◁ C43×C67 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#460×C67 | C2 | semidirect |
| 3. C42×Q8×C67 | C2 | semidirect |
| 4. C67×#1982 | C2 | semidirect |
| 5. C67×#1842 | C2 | semidirect |
| 29. C4×Q8×C67 | D4 | semidirect |
| 63. C42×C67 | SD16 | semidirect |
| 71. Q8×C67 | #127 | semidirect |
| 96. C4×C67 | #460 | semidirect |
| 99. #33161 | C67 | direct (N × H) |
| 104. C2×#460 | C2×C67 | semidirect |
| 106. C42×Q8 | C2×C67 | semidirect |
| 107. #1982 | C2×C67 | semidirect |
| 108. #1842 | C2×C67 | semidirect |
| 109. C67 | #33161 | direct (N × H) |
| 133. C4×Q8 | D4×C67 | semidirect |
| 167. C42 | SD16×C67 | semidirect |
| 175. Q8 | #127×C67 | semidirect |
| 200. C4 | #460×C67 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#460×C67 | 2 |
| C67×#2867 | 2 |
| C42×Q8×C67 | 2 |
| C67×#1982 | 2 |
| C67×#1842 | 2 |
| #33161 | 67 |