Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
1506 conjugacy classes of subgroups; only the 366 normal subgroups are shown.
This group has 1506 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 |
| 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×#459×C67 | C2 | semidirect |
| 2. C67×#2867 | C2 | semidirect |
| 3. C42×D4×C67 | C2 | semidirect |
| 4. C67×#1982 | C2 | semidirect |
| 5. C67×#1842 | C2 | semidirect |
| 30. C4×D4×C67 | D4 | semidirect |
| 66. C42×C67 | D8 | semidirect |
| 81. D4×C67 | #127 | semidirect |
| 105. C4×C67 | #459 | semidirect |
| 108. #33160 | C67 | direct (N × H) |
| 114. C2×#459 | C2×C67 | semidirect |
| 115. #2867 | C2×C67 | semidirect |
| 116. C42×D4 | C2×C67 | semidirect |
| 117. #1982 | C2×C67 | semidirect |
| 118. #1842 | C2×C67 | semidirect |
| 119. C67 | #33160 | direct (N × H) |
| 144. C4×D4 | D4×C67 | semidirect |
| 180. C42 | D8×C67 | semidirect |
| 195. D4 | #127×C67 | semidirect |
| 219. C4 | #459×C67 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#459×C67 | 2 |
| C67×#2867 | 2 |
| C42×D4×C67 | 2 |
| C67×#1982 | 2 |
| C67×#1842 | 2 |
| #33160 | 67 |