Finite Group DatabasebetaFinite Group DatabasebetaOrder 23488.
198 conjugacy classes of subgroups; only the 62 normal subgroups are shown.
This group has 198 conjugacy classes of subgroups — too many to draw. Only its 62 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C367 | C2×D4 |
| commutator, Frattini, cosocle | C2×C4 | C23×C367 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C367 ◁ C22×C4×C367 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C22×D4×C367 | C2 | semidirect |
| 2. C2×D8×C367 | C2 | semidirect |
| 3. #121×C367 | C2 | semidirect |
| 4. #102×C367 | C2 | semidirect |
| 5. C22⋊C8×C367 | C2 | semidirect |
| 11. C2×D4×C367 | C22 | semidirect |
| 14. C2×C8×C367 | C22 | semidirect |
| 15. C4⋊C4×C367 | C22 | semidirect |
| 27. D4×C367 | D4 | semidirect |
| 42. C22×C367 | D8 | semidirect |
| 53. C367 | #447 | direct (N × H) |
| 54. #447 | C367 | direct (N × H) |
| 55. C22×D4 | C2×C367 | semidirect |
| 56. C2×D8 | C2×C367 | semidirect |
| 57. #121 | C2×C367 | semidirect |
| 58. #102 | C2×C367 | semidirect |
| 59. C22⋊C8 | C2×C367 | semidirect |
| 65. C2×D4 | C22×C367 | semidirect |
| 68. C2×C8 | C22×C367 | semidirect |
| 69. C4⋊C4 | C22×C367 | semidirect |
| 81. D4 | D4×C367 | semidirect |
| 96. C22 | D8×C367 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D4×C367 | 2 |
| C2×D8×C367 | 2 |
| #121×C367 | 2 |
| #102×C367 | 2 |
| C22⋊C8×C367 | 2 |
| #447 | 367 |