Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
188 conjugacy classes of subgroups; only the 70 normal subgroups are shown.
This group has 188 conjugacy classes of subgroups — too many to draw. Only its 70 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C67 | #2215 |
| commutator, Frattini, cosocle | C2×C16 | C23×C67 |
| LCS | G ▷ C2×C16 ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C67 ◁ C2×C4×C67 ◁ #131×C67 ◁ #504×C67 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×D32×C67 | C2 | semidirect |
| 2. C67×#2258 | C2 | semidirect |
| 3. C67×#2221 | C2 | semidirect |
| 4. C67×#1425 | C2 | semidirect |
| 5. C67×#1419 | C2 | semidirect |
| 64. #13700 | C67 | direct (N × H) |
| 69. C2×D32 | C2×C67 | semidirect |
| 70. #2258 | C2×C67 | semidirect |
| 71. #2221 | C2×C67 | semidirect |
| 72. #1425 | C2×C67 | semidirect |
| 73. #1419 | C2×C67 | semidirect |
| 74. C67 | #13700 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D32×C67 | 2 |
| C67×#2258 | 2 |
| C67×#2221 | 2 |
| C67×#1425 | 2 |
| C67×#1419 | 2 |
| #13700 | 67 |